Screening for fluctuating energy relaxation times

ABSTRACT

One or more systems, devices, computer program products and/or computer-implemented methods of use provided herein relate to determining estimated true relaxation times of qubits absent measurement of entire T 1  decay times of the qubits. A system can comprise a memory that stores computer executable components; and a processor that executes the computer executable components stored in the memory, wherein the computer executable components are executable to cause, by the processor, one or more energy relaxation measurements, using a pulse generation, at the qubit frequency for a qubit and at a plurality of shifted frequencies for the qubit, and to determine, by the processor, a true average relaxation time of the qubit based on the plurality of energy relaxation measurements.

BACKGROUND

Quantum computing is generally the use of quantum-mechanical phenomenato perform computing and information processing functions. Quantumcomputing can be viewed in contrast to classical computing, whichgenerally operates on binary values with transistors. That is, whileclassical computers can operate on bit values that are either 0 or 1,quantum computers operate on quantum bits (qubits) that comprisesuperpositions of both 0 and 1. Quantum computing has the potential tosolve problems that, due to computational complexity, cannot be solvedor can only be solved slowly on a classical computer.

On a large scale, quantum computing cloud service providers can executemillions of quantum jobs for users during a year. Each quantum job caninclude the execution of one or more quantum programs at a physicallogic circuit. Physical, real-world, quantum logic circuits controlledby a quantum system can include a plurality of qubits.

SUMMARY

The following presents a summary to provide a basic understanding of oneor more embodiments described herein. This summary is not intended toidentify key or critical elements, delineate scope of particularembodiments or scope of claims. Its sole purpose is to present conceptsin a simplified form as a prelude to the more detailed description thatis presented later. In one or more embodiments described herein,systems, computer-implemented methods, apparatus and/or computer programproducts facilitate a process to analyze coherence parameters ofphysical qubits of a real-world physical qubit layout of a quantumcomputer.

In accordance with an embodiment, a system can comprise a memory thatstores computer executable components, and a processor that executes thecomputer executable components stored in the memory, wherein thecomputer executable components are executable to cause, by theprocessor, one or more energy relaxation measurements, using a pulsegeneration, at the qubit frequency for a qubit and at a plurality ofshifted frequencies for the qubit, and to determine, by the processor, atrue average relaxation time of the qubit based on the plurality ofenergy relaxation measurements.

In accordance with another embodiment, a computer-implemented method cancomprise measuring, by a system operatively coupled to a processor, aplurality of energy relaxation measurements comprising at least onemeasurement at a qubit frequency for a qubit and one or moremeasurements at one or more shifted frequencies for the qubit, anddetermining, by the system, an estimation of a true average relaxationtime of the qubit based on the plurality of energy relaxationmeasurements.

In accordance with yet another embodiment, a computer program productfacilitating a process to determine an estimated true relaxation time ofa qubit can comprise a computer readable storage medium having programinstructions embodied therewith. The program instructions can beexecutable by a processor to cause the processor to measure, by theprocessor, a plurality of energy relaxation measurements comprising atleast one measurement at a qubit frequency for a qubit and one or moremeasurements at one or more shifted frequencies for the qubit, and todetermine, by the processor, an estimation of a true average relaxationtime of the qubit based on the plurality of energy relaxationmeasurements.

An advantage of the aforementioned system, computer-implemented methodand/or computer program product can be an increase in understanding ofqubit coherence parameters and of fluctuations in the qubit coherenceparameters, and the subsequent ability to employ that information toprovide a rapid forecast of qubit useability for an execution of aquantum program. Further advantages can comprise an ability to rapidlyplot energy relaxation of qubits over a plurality of shifted frequenciesrelative to the qubit frequencies, and along a range of real time, suchas days, weeks and/or months. This plot can enable understanding of thedynamic frequency space of a qubit.

Yet another advantage of the aforementioned system, computer-implementedmethod and/or computer program product can be ability to use any of fluxtuning, Autler-Townes effect, DC electric field, mechanical strainand/or other suitable method to shift a qubit's frequency for probingthe frequency space about the qubit frequency of the qubit. As usedherein, the Autler-Townes effect/shift/tone can also be referred to asthe Autler-Townes-AC-Stark effect/shift/tone or AC Starkeffect/shift/tone.

DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a block diagram of an example, non-limiting systemthat can facilitate a process to determine an estimated true relaxationtime of a qubit, in accordance with one or more embodiments describedherein.

FIG. 2 illustrates a block diagram of another example, non-limitingsystem that can facilitate a process to determine an estimated truerelaxation time of a qubit, in accordance with one or more embodimentsdescribed herein.

FIG. 3 illustrates a plot of a P₁ probability landscape of a singlequbit, the plot comprising a range of applied Autler-Townes tones ofvarying frequency and fixed power/amplitude graphed against time, inaccordance with one or more embodiments described herein.

FIG. 4 illustrates a graph of proof of concept of conventionallyacquired T₁ and P₁ values graphed against <T₁> (T₁ averages) and <P₁>(P₁ average) of various qubits of a qubit device, in accordance with oneor more embodiments described herein.

FIG. 5A illustrates a graph resulting from energy relaxationspectroscopy employing an Autler-Townes effect (AT effect) to shift aqubit frequency.

FIG. 5B illustrates a pair of pulse sequences that can be employed bythe non-limiting system of FIG. 2 , and particularly employing an ATtone, in accordance with one or more embodiments described herein.

FIG. 6 illustrates a set of graphs demonstrating outcomes of employmentof energy relaxation spectroscopy by the non-limiting system of FIG. 2 ,via employment of an AT tone to shift qubit frequencies, in accordancewith one or more embodiments described herein.

FIG. 7 illustrates a process flow for facilitating a process todetermine an estimated true relaxation time of a qubit, in accordancewith one or more embodiments described herein.

FIG. 8 illustrates a block diagram of an example, non-limiting,operating environment in which one or more embodiments described hereincan be facilitated.

FIG. 9 illustrates a block diagram of an example, non-limiting, cloudcomputing environment in accordance with one or more embodimentsdescribed herein.

FIG. 10 illustrates a block diagram of example, non-limiting,abstraction model layers in accordance with one or more embodimentsdescribed herein.

DETAILED DESCRIPTION

The following detailed description is merely illustrative and is notintended to limit embodiments and/or application or utilization ofembodiments. Furthermore, there is no intention to be bound by anyexpressed or implied information presented in the preceding Summarysection, or in the Detailed Description section. One or more embodimentsare now described with reference to the drawings, wherein like referencenumerals are utilized to refer to like elements throughout. In thefollowing description, for purposes of explanation, numerous specificdetails are set forth in order to provide a more thorough understandingof the one or more embodiments. It is evident, however, in variouscases, that the one or more embodiments can be practiced without thesespecific details.

As used herein, a quantum circuit can be a set of operations, such asgates, performed on a set of real-world physical qubits with the purposeof obtaining one or more qubit measurements. A quantum processor cancomprise the one or more real-world physical qubits.

Qubit states only can exist (or can only be coherent) for a limitedamount of time. Thus, an objective of operation of a quantum logiccircuit (e.g., including one or more qubits) can be to maximize thecoherence time of the employed qubits. Time spent to operate the quantumlogic circuit can undesirably reduce the available time of operation onone or more qubits. This can be due to the available coherence time ofthe one or more qubits prior to decoherence of the one or more qubits.For example, a qubit state can be lost in less than 100 to 200microseconds in one or more cases.

Operation of the quantum circuit can be facilitated, such as by awaveform generator, to produce one or more physical pulses and/or otherwaveforms, signals and/or frequencies to alter one or more states of oneor more of the physical qubits. The altered states can be measured, thusallowing for one or more computations to be performed regarding thequbits and/or the respective altered states.

Operations on qubits generally can introduce some error, such as somelevel of decoherence and/or some level of quantum noise, furtheraffecting qubit availability. Quantum noise can refer to noiseattributable to the discrete and/or probabilistic natures of quantuminteractions.

A T₁ (energy relaxation time) of a qubit can fluctuate in time. Onesource of the fluctuations can be the quantum noise. One type of quantumnoise can be defects called two level systems (TLS). A two level systemhas a transition energy (or corresponding frequency). When a TLS isresonant with the qubit frequency, the rate of energy relaxation canincrease, leading to shorter T₁.

A two-level system (TLS), among other noise causes, can comprise asource of noise that can cause deterioration of coherence parameters(e.g., shorter T₁) of one or more qubits of a quantum logic circuit.TLSs are believed to be able to coherently or incoherently couple to thequbit leading to either faster energy relaxation times or rate of energydecay (e.g., shorter T₁s corresponding to an exponential 1/e decay time)as well as faster phase decoherence (e.g., T₂). That is, the noise cancouple to a low-energy thermal fluctuator, for example, which canrandomly change the TLS energy resonance (or the equivalent frequency ofthe TLS resonance). A TLS can spectrally diffuse into and out ofresonance with the qubit frequency when the TLS is in the vicinity of aqubit frequency. This is a source of T₁ fluctuation at the qubitfrequency.

The qubit frequency is the resonance frequency of a qubit energytransition between two states such as, but not limited to, the groundand first excited states of the qubit. The vicinity of a qubit frequencyis a frequency range which in some embodiments can range from about 10megahertz (MHz) below the qubit frequency to about 10 MHz above thequbit frequency. In other embodiments, the vicinity of a qubit frequencycan range from about 100 MHz below the qubit frequency to about 100 MHzabove the qubit frequency. In still other embodiments, the vicinity of aqubit frequency can range from about 1 gigahertz (GHz) below the qubitfrequency to about 1 GHz above the qubit frequency. Without beinglimited to theory, it is believed that such two-level systems can becaused by atomic scale defects in surface oxides on the metals and/or onthe silicon of a physical real-world qubit and can beelectromagnetically active. Indeed, a qubit, such as a transmon itselfis a resonator with an electromagnetic excitation, and thus a qubitexcitation can couple with a two-level system (TLS) and can causeperformance issues for a quantum logic circuit, such as, but not limitedto, deterioration of qubit parameters.

Due to presence of two-level systems in/at the quantum system and/or dueto maintenance and/or diagnostics to be performed relative to coherencetimes of a particular qubit, one or more qubits, such as superconductingqubits, can be unavailable and/or not recommended for use with thequantum logic circuit, even if desired for use. Furthermore, absentunderstanding of such two-level systems and their associatedfluctuations relative to the frequency domain of one or more qubits of aquantum system, coherence of the qubit can be affected. Loss ofcoherence can cause failure of execution of a quantum circuit, thuswasting power, time, queue space and/or memory relative to a queue ofjobs to be performed on a respective quantum system.

There can be varying causes for loss of qubit coherence. Some causes ofdecoherence can be equipment related. When coherence of a qubit suddenlychanges, or changes gradually over time, one or more existing solutionscan comprise not employing the qubit until the coherence deteriorationis reduced or ends altogether, such as compared to historical coherenceparameters for the particular qubit. Absent understanding, such asdefinitive understanding, that the change in qubit coherence parametersis caused by a two-level system, unnecessary diagnostics and/ormaintenance can be performed, such as switching out cables, swappingcontrol electronics, warming up a super-cooled refrigeration system ofthe quantum system to troubleshoot components, and/or the like. Also,even when a TLS is suspected as a culprit of noise issues, existingtechniques for analyzing the frequency space about a qubit's unperturbedfrequency, can be cumbersome, timely, resource intensive, and/ormanually intensive relative to at least the scheduling and operation ofassociated diagnostics. The unperturbed frequency of the qubit is theresonance frequency of the qubit as fabricated, in the absence ofexternal effects that may shift its frequency, including but not limitedto magnetic flux bias, DC electric field, mechanical strain, and/or anAutler-Townes (AT) effect.

In view of unintended or unforeseen decoherence, waste of quantumresources, time, power, and/or labor can occur. Indeed, because quantumprocessors and quantum systems are scarce and costly resources, suchwaste can be detrimental to both users and administrators of quantumsystems. Put another way, each quantum processor can have a fixed numberof qubits it supports. When quantum circuits cannot use the fullcapacity of a quantum processor, one or more qubits can remain idle.Thus, it can be desired to facilitate a process for understandingdeteriorations and/or changes in qubit coherence parameters to in turnprovide more informed queuing of quantum jobs and/or mapping of quantumcircuits of the quantum jobs.

Moreover, different quantum circuits can require varying resources. Forexample, one quantum circuit can use different physical qubits of aquantum logic circuit of a respective quantum system than anotherquantum circuit. During scheduling of quantum jobs from a queue andcorresponding mapping of quantum circuits to a quantum logic circuit,particular qubits can be desirable for use with one quantum circuit ascompared to other qubits of a same quantum logic circuit. Quantum noise,such as two-level systems can therefore interfere, often unknowingly,with this mapping. Therefore, device designs that can target qubitshaving a longer lifetime of their respective quantum states and/orhaving longer coherence time can be desirable.

To address the aforementioned presence of two-level systems, lack ofinformation regarding qubit coherence parameters, and/ordiagnostics/maintenance to address noise, described herein are one ormore embodiments of a system, computer-implemented method and/orcomputer program product that can analyze the frequency space of aqubit, to allow for better understanding and/or prediction of evolvingcoherence parameters of the qubit. Indeed, the one or more embodimentsdescribed herein can account for one or more deficiencies of existingtechniques for analyzing qubit coherence parameters of one or morequbits, including both fixed frequency and multi-junction qubits.

With respect to single junction qubits, such as single Josephsonjunction transmons with fixed frequency couplings, such type of qubitrepresents a device architecture that can be employed in a device havingeven 60 or more qubits, for example. The single junction configurationcan offer advantages such as reduced sensitivity to flux noise, whilepreserving the transmon charge insensitivity and reducing systemcomplexity with few control inputs (e.g., due to the single junctions).However, due to the limited frequency tunability of single junctionqubits, existing TLS spectroscopy techniques are limited, cumbersomeand/or time-consuming.

Generally, provided are one or more embodiments of a system,computer-implemented method and/or computer program product that canfacilitate a process to employ an excited qubit shifted in frequency asa probe the energy relaxation rate frequencies at or around the qubit'sfrequency. Understanding this neighborhood (i.e., vicinity) can allowfor one or more determinations to be made regarding coherence parametersof the qubit at different shifted frequencies, such as specificallybased on TLS and/or noise presence about a qubit frequency over a rangeof time, such as days, weeks and/or months. This can be desiredinformation when determining which qubits and/or which qubit device toemploy for executing a quantum circuit due to the nature of qubitcoherence parameters being dynamic, fluctuating and/or otherwisechanging when in the presence of or coming into at least partialresonance with a TLS and/or other system noise. Indeed, suchunderstanding can be gained, such as separately on a qubit-by-qubitbasis, to gain an understanding regarding frequency space about a groupof qubits of a quantum processor or other quantum device. A qubit devicecomprises a group of qubits pertaining to the same piece of hardware.

Generally, the one or more systems, devices, computer program productsand/or computer-implemented methods of use provided herein can employ aqubit shifted in frequency, such as by a frequency shifting method basedon flux tuning, an Autler-Townes off-resonant tone (AT tone), DCelectric field, mechanical strain, and/or by another suitable method toprobe a frequency space about excitation frequencies of the qubit.Results of the probing can be employed to determine probabilities of thequbit being at one or more excited states at various times and/orvarious shifted frequencies.

Further, results of the probing can be employed to forecast estimatedtrue relaxation times of a qubit at one or more frequencies based on thefrequency neighborhood about the desired one or more frequencies.Understanding of variance in the probabilities can allow for a betterunderstanding of whether or not to employ the qubit, and or a respectivequbit device comprising the qubit, such as relative to one or more otherqubits and/or qubit devices. These one or more systems, device, computerprogram products and/or computer-implemented methods of use can beemployed relative to plural qubits of a qubit device. It is noted thatwhile one or more operations described herein can be employed absentapplication of flux bias to the qubits (e.g., absent flux tuning of thequbits) to determine the aforementioned information and results, suchoperations can function by instead employing flux bias, mechanicalstrain and/or DC electric field to shift a qubit frequency.

The information can be gained more quickly than by employing existingtechniques relying on T₁ measurements made at only the unshifted qubitfrequency, where is the unperturbed/unshifted qubit frequency. The T₁fluctuates slowly in time. An estimate of the ‘true’<T₁> is typicallyobtained by measuring then waiting a time (i.e., best if that time islong relative to any correlation time of the T₁ fluctuations). Obtainingan average of T₁ with a small uncertainty requires many measurementsspaced by a long time. As used herein, T₁ refers to energy relaxationtime of a qubit, which is a coherence time limitation on how longinformation can be stored in the qubit. The measurement of T₁(Δω) formany different Δω further provides an understanding about movements andfluctuations in the respective frequency space, better forecasting canbe provided using the one or more embodiments described herein.

One or more embodiments are now described with reference to thedrawings, where like referenced numerals are used to refer to likeelements throughout. As used herein, the terms “entity”, “requestingentity” and “user entity” can refer to a machine, device, component,hardware, software, smart device and/or human. In the followingdescription, for purposes of explanation, numerous specific details areset forth in order to provide a more thorough understanding of the oneor more embodiments. It is evident, however, in various cases, that theone or more embodiments can be practiced without these specific details.

Further, the embodiments depicted in one or more figures describedherein are for illustration only, and as such, the architecture ofembodiments is not limited to the systems, devices and/or componentsdepicted therein, nor to any particular order, connection and/orcoupling of systems, devices and/or components depicted therein. Forexample, in one or more embodiments, the non-limiting systems describedherein, such as non-limiting systems 100 and/or 200 as illustrated atFIGS. 1 and 2 , and/or systems thereof, can further comprise, beassociated with and/or be coupled to one or more computer and/orcomputing-based elements described herein with reference to an operatingenvironment, such as the operating environment 800 illustrated at FIG. 8. In one or more described embodiments, computer and/or computing-basedelements can be used in connection with implementing one or more of thesystems, devices, components and/or computer-implemented operationsshown and/or described in connection with FIGS. 1 and/or 2 and/or withother figures described herein.

Turning first generally to FIG. 1 , one or more embodiments describedherein can include one or more devices, systems and/or apparatuses thatcan facilitate a process to determine an estimated true relaxation timeof a qubit, as briefly described above. For example, FIG. 1 illustratesa block diagram of an example, non-limiting system 100 that can employ ashifting component to probe frequency space of a qubit of a quantumlogic circuit of a quantum system. As used herein, the “true” relaxationtime is the ideal relaxation time being the true mean of a continuousdistribution.

At FIG. 1 , illustrated is a block diagram of an example, non-limitingsystem 100 that can facilitate such probing process, in accordance withone or more embodiments described herein. While referring here to one ormore processes, facilitations and/or uses of the non-limiting system100, description provided herein, both above and below, also can berelevant to one or more other non-limiting systems described herein,such as the non-limiting system 200, to be described below in detail.

As illustrated at FIG. 1 , the non-limiting system 100 can comprise aclassical system 131 and a quantum system 101. The quantum system 101can comprise at least a quantum processor 106 having a quantum logiccircuit 118 comprising at least one or more qubits. The classical system131 can comprise one or more components, such as a memory 134, quantumprocessor 136, bus 136, measurement component 142 and/or weightingcomponent 144.

Generally, classical system 131, such as a qubit energy relaxationscreening (QERS) system 131, can employ the measurement component 442 todetermine one or more energy relaxation measurements at the qubitfrequency for a qubit. The measurement component likewise can determineone or more energy relaxation measurements at a plurality of shiftedfrequencies for the qubit. By combining these measurements, e.g., at theestimation component, such as by averaging these measurements, oraveraging these measurements according to weights of the measurements,an estimation of a true average relaxation time of the qubit can beobtained. That is, incorporated in the estimation are a range ofmeasurements through frequencies through which noise (e.g., two levelsystems) can move and or fluctuate before migrating/fluctuating/jumpingto the qubit frequency.

Turning next to FIG. 2 , the figure illustrates a diagram of an example,non-limiting system 200 that can facilitate TLS and qubit excitationspectroscopy and subsequent analysis of the results, therebyfacilitating a process to determine an estimated true relaxation time ofa qubit. For example, FIG. 2 illustrates a block diagram of an example,non-limiting system 200 that can employ a shifting component to affect aqubit 217, and a readout component 214 that can be employed to measureone or more characteristics of the affected qubit 217. In response, thenon-limiting system 200 can employ a measurement component 242 todetermine one or more estimations of true average relaxation times(<T₁>_(δω)), where δω) refers to the frequency range covered by theaverage employed in the estimation, ranging from frequency value −δω⁻ to−δω₊.

Generally, the non-limiting system can first obtain T₁ measurements atmultiple offset frequencies, used for obtaining the estimator describedherein, <T₁>_(δω)), via any suitable means. Again, as used herein, T₁refers to energy relaxation time of a qubit, which is a coherence timelimitation on how long information can be stored in the qubit. Thesuitable means for measuring the T₁s can include a slow method ofentirely measuring T₁s (i.e., P₁s at different delay times) and atvarying frequencies, using DC electric field, using mechanical strain,or by flux tuning multi-junction qubits to various shifted frequenciesand waiting for measurements of entire T₁s. Additionally, T₁s can bemeasured by employing the qubit as a probe in frequency space todetermine probabilities P₁ of a qubit being in a particular state at aparticular time. From the P₁s, T₁s can be obtained. This method isgenerally described relative to FIGS. 5A-6 . This method describedherein for first obtaining the T₁s can provide more rapid results thanthe other methods indicated above—the method described herein byemploying P₁ as a proxy for time-to-decoherence (T₁) of the particularqubit, such as at a fixed delay time. Nonetheless, the other methodsindicated above (flux tuning, DC electric field, mechanical strain,and/or the like) and understood to one having ordinary skill in the art,can be employed, albeit more slowly providing results, and wastingpower, time, energy and/or manual labor.

Using the P₁ measurements obtained, T₁ measurements can be determined.As compared to waiting for a plurality of P₁ measurements at differentdelay times, at different delay times, τ to more accurately fit theenergy relaxation to, for example, an exponential decay ascribing T₁ tothe 1/e time. The P₁ and T₁s described above are made at a single qubitfrequency offset including 0 offset.

Estimating a true relaxation time, <T₁>, of a qubit is commonly doneusing an average of many weakly time correlated T₁ measurement of thequbit, where Δt is the total time over which the average is made (i.e.,the sum of many time intervals sufficient to produce weak correlation inthe T₁ fluctuations in time). Spacings in time to obtain weaklycorrelated measurements are typically orders of magnitude larger thanthe time to obtain a single T₁ measurement. The techniques describedherein can provide results that better correlate with the unattainable<T₁> (true average T₁). The average according to existing techniques isdenoted as <T₁>_(Δt).

Generally, an estimator <T₁>_(δω) has been surprisingly discovered bythe inventors to be a faster estimator of unattainable <T₁> (trueaverage T₁) than existing techniques for obtaining an estimator ofaverage T₁ (denoted herein as <T₁>). The estimator described herein,<T₁>_(δω), is an estimator for <T₁> that can be obtained more quicklythan the long time averaging necessary to obtain <T₁>_(Δt). Indeed, theestimator described herein, <T₁>_(δω), can instead comprise averaging bytaking T₁ measurements at multiple offset frequencies, Δω_(i), from thequbit frequency, ω_(q), of a qubit, q (ω are expressed typically inRad/s whereas f=ω/(2π) are expressed in Hz). As used herein, “i” is anindex for N different frequencies, where N is the number of differentfrequencies measured.

Repetitive description of like elements and/or processes employed inrespective embodiments is omitted for sake of brevity. As indicatedpreviously, description relative to an embodiment of FIG. 1 can beapplicable to an embodiment of FIG. 2 . Likewise, description relativeto an embodiment of FIG. 2 can be applicable to an embodiment of FIG. 1.

In one or more embodiments, the non-limiting system 200 can be a hybridsystem and thus can include both a quantum system and a classicalsystem, such as a quantum system 201 and a classical-based system 231(also herein referred to as a classical system 231). In one or moreother embodiments, the quantum system 201 can be separate from, butfunction in combination with, the classical system 231. In one or moreembodiments, one or more components of the quantum system 201, such asthe readout component 214, can be at least partially comprised by theclassical system 231, or otherwise comprised external to the quantumsystem 201. In one or more embodiments, one or more components of theclassical system 231, such as the measurement component 242 and/orweighting component 244, can be at least partially comprised by thequantum system 201, or otherwise comprised external to the classicalsystem 231 (also herein referred to as the qubit energy relaxationscreen system 231 or QERS system 231).

One or more communications between one or more components of thenon-limiting system 200 can be facilitated by wired and/or wirelessmeans including, but not limited to, employing a cellular network, awide area network (WAN) (e.g., the Internet), and/or a local areanetwork (LAN). Suitable wired or wireless technologies for facilitatingthe communications can include, without being limited to, wirelessfidelity (Wi-Fi), global system for mobile communications (GSM),universal mobile telecommunications system (UMTS), worldwideinteroperability for microwave access (WiMAX), enhanced general packetradio service (enhanced GPRS), third generation partnership project(3GPP) long term evolution (LTE), third generation partnership project 2(3GPP2) ultra-mobile broadband (UMB), high speed packet access (HSPA),Zigbee and other 802.XX wireless technologies and/or legacytelecommunication technologies, BLUETOOTH®, Session Initiation Protocol(SIP), ZIGBEE®, RF4CE protocol, WirelessHART protocol, 6LoWPAN (Ipv6over Low power Wireless Area Networks), Z-Wave, an ANT, anultra-wideband (UWB) standard protocol and/or other proprietary and/ornon-proprietary communication protocols.

The classical system 231 and/or the quantum system 201 can be associatedwith, such as accessible via, a cloud computing environment 950described below with reference to FIG. 9 and/or with one or morefunctional abstraction layers described below with reference to FIG. 10(e.g., hardware and software layer 1060, virtualization layer 1070,management layer 1080 and/or workloads layer 1090). For example, theclassical system 231 can be associated with a cloud computingenvironment 950 such that aspects of classical processing can bedistributed between the classical system 231 and the cloud computingenvironment 950.

Turning first to the quantum system 201, generally based on a quantumjob request 224, on physical qubit layouts 252, and/or on an associatedqueue of quantum circuits 250 to be executed, the quantum operationcomponent 216 and/or quantum processor 206 can direct execution of thequantum circuits at the quantum logic circuit 218.

Generally, the quantum system 201 (e.g., quantum computer system,superconducting quantum computer system and/or the like) can employquantum algorithms and/or quantum circuitry, including computingcomponents and/or devices, to perform quantum operations and/orfunctions on input data to produce results that can be output to anentity. The quantum circuitry can comprise quantum bits (qubits), suchas multi-bit qubits, physical circuit level components, high levelcomponents and/or functions. The quantum circuitry can comprise physicalpulses that can be structured (e.g., arranged and/or designed) toperform desired quantum functions and/or computations on data (e.g.,input data and/or intermediate data derived from input data) to produceone or more quantum results as an output. The quantum results, e.g.,quantum measurement 240, can be responsive to the quantum job request224 and associated input data and can be based at least in part on theinput data, quantum functions and/or quantum computations.

In one or more embodiments, the quantum system 201 can comprisecomponents, such as a quantum operation component 216, a quantumprocessor 206, shifting component 212 (e.g., a waveform generator)and/or a readout component 214. In other embodiments, the readoutcomponent 214 can be comprised at least partially by the classicalsystem 231 and/or be external to the quantum system 201. The quantumprocessor 206 can comprise the quantum logic circuit 218 comprising oneor more, such as plural, qubits 217. Individual qubits 217A, 217B and217C, for example, can be fixed frequency and/or single junction qubits,such as transmon qubits.

The quantum processor 206 can be any suitable processor. The quantumprocessor 206 can generate one or more instructions for controlling theone or more processes of the quantum operation component 216 and/or forcontrolling the quantum logic circuit 218.

The quantum operation component 216 can obtain (e.g., download, receive,search for and/or the like) a quantum job request 224 requestingexecution of one or more quantum programs 250 and/or a physical qubitlayout 252 generated by the classical system 231. The quantum jobrequest 224 can be provided in any suitable format, such as a textformat, binary format and/or another suitable format. In one or moreembodiments, the quantum job request 224 can be received by a componentother than of the quantum system 201, such as a by a component of theclassical system 231.

The quantum operation component 216 can determine one or more quantumlogic circuits, such as the quantum logic circuit 218, for executing aquantum program. In one or more embodiments, the quantum operationcomponent 216/quantum processor 206 can direct the shifting component212 to generate one or more pulses, tones, waveforms and/or the like toaffect one or more qubits 217.

The shifting component 212 can generally perform one or more quantumprocesses, calculations and/or measurements for shifting the frequencyof one or more qubits 217, such as when in respective excited states.For example, the shifting component 212 can operate one or more qubiteffectors, such as qubit oscillators, harmonic oscillators, pulsegenerators and/or the like to cause one or more pulses to stimulateand/or manipulate the state(s) of the one or more qubits 217 comprisedby the quantum system 201, and thus can be and/or comprise a waveformgenerator. In one or more other embodiments, additionally and/oralternatively, the shifting component 212 can facilitate application offlux bias/flux tuning to one or more qubits. This shifting can beemployed, as briefly described above, relative to probing of frequencyspace about the qubit frequency of the qubit, to thereby facilitatemeasurement of one or more qubit parameters at the shifted frequency.

The readout component 214 can facilitate transmission, e.g., readout, ofone or more readings, signals and/or the like to the classical system,such as to the measurement component 242. From the readout, themeasurement component can determine one or more energy relaxationmeasurements at the qubit frequency or at a shifted frequency of thequbit.

The quantum logic circuit 218 and a portion or all of the shiftingcomponent 212 can be contained in a cryogenic environment, such asgenerated by a cryogenic chamber 225, such as a dilution refrigerator.Indeed, a signal can be generated by the shifting component 212 withinthe cryogenic chamber 225 to affect one or more of the plurality ofqubits 217. Where the plurality of qubits 217 are superconductingqubits, cryogenic temperatures, such as about 4K or lower can beemployed to facilitate function of these physical qubits. Accordingly,one or more elements of the readout component 214 also can beconstructed to perform at such cryogenic temperatures.

The readout component 214, or at least a portion thereof, can becontained in the cryogenic chamber 225, such as for reading a state,frequency and/or other characteristic of qubit, excited, decaying orotherwise.

Generally, the operations can allow for better understanding and/orplanning of the quantum job queue, qubit decay and/or qubit coherencerelative to the quantum logic circuit 218. As indicated, the diagnosticsand operations of the quantum system 201 can be performed at anysuitable interval to thereby facilitate the frequency space mapping ofone or more of the qubits 217. As indicated, a suitable interval can bebetween execution of quantum jobs and/or at a defined and uniforminterval, such as every 6 hours, every 3 hours, every 1 hour and/or anyother suitable interval. The diagnostic processes to be discussed can beperformed on any number, one or more, of the qubits 217 of the quantumlogic circuit 218 to gain a better understanding of frequency spaceabout the qubit frequencies of these qubits 217.

Further, the aforementioned description(s) refer(s) to the operation ofa single set of diagnostics run on a single qubit. However, employmentof the diagnostics can be facilitated, where suitable at one or morequbits at a time of a quantum system. For example, non-neighbor qubitsof a qubit logic circuit can be simultaneously measured.

Next, discussion turns to operations of the classical system 231 thatcan be performed on and/or employing the readout output from the quantumsystem 201, to thereby facilitate generation of the informationregarding the frequency space of the qubit, over a range of time thatcan span days, weeks and/or months.

Turning now to the classical system specifically, generally, theclassical system 231 can comprise any suitable type of component,machine, device, facility, apparatus and/or instrument that comprises aprocessor and/or can be capable of effective and/or operativecommunication with a wired and/or wireless network. All such embodimentsare envisioned. For example, the classical system 231 can comprise aserver device, computing device, general-purpose computer,special-purpose computer, quantum computing device (e.g., a quantumcomputer), tablet computing device, handheld device, server classcomputing machine and/or database, laptop computer, notebook computer,desktop computer, cell phone, smart phone, consumer appliance and/orinstrumentation, industrial and/or commercial device, digital assistant,multimedia Internet enabled phone, multimedia players and/or anothertype of device and/or computing device. Likewise, the classical system231 can be disposed and/or run at any suitable device, such as, but notlimited to a server device, computing device, general-purpose computer,special-purpose computer, quantum computing device (e.g., a quantumcomputer), tablet computing device, handheld device, server classcomputing machine and/or database, laptop computer, notebook computer,desktop computer, cell phone, smart phone, consumer appliance and/orinstrumentation, industrial and/or commercial device, digital assistant,multimedia Internet enabled phone, multimedia players and/or anothertype of device and/or computing device.

The classical system 231 can comprise a plurality of components. Thecomponents can include a memory 234, processor 236, bus 235, mappingcomponent 232, scheduler component 238, measurement component 242,estimation component 246 and/or weighting component 244. It is notedthat while the measurement component 242, estimation component 246and/or weighting component 244 are shown as being comprised by theclassical system 231, in one or more other embodiments, any one or moreof these components can be comprised by the quantum system 201 or beexternal to the at least partially external to the classical system 231.

Generally, the classical system 231 can facilitate receipt of a quantumjob request 224 and/or receipt of one or more quantum circuits 250 to beoperated on the quantum system 201 relative to the quantum logic circuit218 of the quantum system 201. The quantum circuits 250 can be mapped toone or more physical qubit layouts 252 by the classical system 231, suchas based on the readout data from the quantum system 201 and furtherbased on the use of that readout data by the measurement component 242of the classical system.

Discussion first turns briefly to the processor 236, memory 234 and bus235 of the classical system 231. For example, in one or moreembodiments, the classical system 231 can comprise the processor 236(e.g., computer processing unit, microprocessor, classical processor,quantum processor and/or like processor). In one or more embodiments, acomponent associated with classical system 231, as described herein withor without reference to the one or more figures of the one or moreembodiments, can comprise one or more computer and/or machine readable,writable and/or executable components and/or instructions that can beexecuted by processor 236 to facilitate performance of one or moreprocesses defined by such component(s) and/or instruction(s). In one ormore embodiments, the processor 236 can comprise the mapping component232, scheduler component 238, measurement component 242, estimationcomponent 246 and/or weighting component 244.

In one or more embodiments, the classical system 231 can comprise thecomputer-readable memory 234 that can be operably connected to theprocessor 236. The memory 234 can store computer-executable instructionsthat, upon execution by the processor 236, can cause the processor 236and/or one or more other components of the classical system 231 (e.g.,mapping component 232, scheduler component 238, measurement component242, estimation component 246 and/or weighting component 244) to performone or more actions. In one or more embodiments, the memory 234 canstore computer-executable components (e.g., mapping component 232,scheduler component 238, measurement component 242, estimation component246 and/or weighting component 244).

The classical system 231 and/or a component thereof as described herein,can be communicatively, electrically, operatively, optically and/orotherwise coupled to one another via a bus 235. Bus 235 can comprise oneor more of a memory bus, memory controller, peripheral bus, externalbus, local bus, quantum bus and/or another type of bus that can employone or more bus architectures. One or more of these examples of bus 235can be employed.

In one or more embodiments, the classical system 231 can be coupled(e.g., communicatively, electrically, operatively, optically and/or likefunction) to one or more external systems (e.g., a non-illustratedelectrical output production system, one or more output targets, anoutput target controller and/or the like), sources and/or devices (e.g.,classical and/or quantum computing devices, communication devices and/orlike devices), such as via a network. In one or more embodiments, one ormore of the components of the classical system 231 and/or of thenon-limiting system 200 can reside in the cloud, and/or can residelocally in a local computing environment (e.g., at a specifiedlocation(s)).

In addition to the processor 236 and/or memory 234 described above, theclassical system 231 can comprise one or more computer and/or machinereadable, writable and/or executable components and/or instructionsthat, when executed by processor 236, can facilitate performance of oneor more operations defined by such component(s) and/or instruction(s).

Turning now to the additional components of the classical system 231(e.g., the mapping component 232, scheduler component 238, measurementcomponent 242, estimation component 246 and/or weighting component 244),generally, quantum circuits 250 received and/or obtained by theclassical system 231 can be analyzed, such as by one or both of themapping component 232 and scheduler component 238. Based on informationfrom the quantum system 201, the mapping component 232 can map a quantumcircuit 250 to a physical qubit layout 252 of the quantum processor 206(e.g., of one or more qubits of the quantum logic circuit 218). Thescheduler component 238, based on additional information from thequantum system 201 and on the mapping information from the mappingcomponent 232, can schedule execution of the quantum circuits 250 in aqueue. The additional information from the quantum system 201 cancomprise times for running iterations of quantum circuits, times fordiagnostic checks, setup, calibration and/or maintenance, and/or thelike.

This mapping can be facilitated based on which one or more qubits 217can be available for execution absent interruption by a TLS and/or othernoise of the frequency space about the qubit frequency and/or about ashifted frequency to which the qubit will be moved during an executionof a quantum program 250.

It also is noted that the processor 236 and/or another component of theclassical system 231 can facilitate one or more of the operations of thequantum system 201. For example, the processor 236, via transmission ofone or more signals to the quantum system 201, can cause the one or moreenergy relaxation measurements, such as using a pulse generation by theshifting component 212. One or more of such instructions can be includedin one or more scheduling and/or mapping instructions, such as providedby the respective scheduler component 238 and/or mapping component 232,provided to the quantum system 201.

The following description(s) refer(s) to a single set of operationsrelative to a single qubit. However, employment of the operations of theclassical system 231 can be facilitated, where suitable for one or morequbits at a time of a quantum system. For example, measurements can betaken, and estimations performed relative to one or more qubits at atime and/or relative to one or more time ranges for one or more qubitsat a time.

Turning now to FIGS. 3 and 4 , one or more operations that can beexecuted and facilitated by the classical system 231 of the non-limitingsystem 200 will be described. The operations can comprise determiningone or more energy relaxation measurements at the qubit frequency for aqubit, determining one or more energy relaxation measurements at aplurality of shifted frequencies for the qubit, estimating a trueaverage relaxation time of the qubit based on the plurality of energyrelaxation measurements, and/or applying weights to one or more of theenergy relaxation measurements.

Turning first to FIG. 3 , a representative plot 300 illustrates repeatline traces of repeated spectral scans, taken approximately once every3-4 hours, extended over hundreds of hours for a particular qubit. Notethat Δω_(i) is referred to as Δω_(q) in FIGS. 3 and 5 . Relative to FIG.2 , the measurement component 242 can generate the plot 300, forexample, from a plurality of T₁ measurements from a plurality of thespectral scans. Again, the T₁ measurements can be gained based on anysuitable qubit frequency shifting method, as described above.

At plot 300, the spectral representation was obtained using a qubitfrequency shifting method based on an Autler-Townes (AT) tone to shiftthe qubit. Particularly, a single decay probability at about τ=50 μs wasused as a proxy for T₁. An estimator of single T₁ measurements can bemade from the single P₁ value, assuming an exponential decay, such as bythe measurement component 242. For example, the measurement component242 can employ Equation 1.

$\begin{matrix}{T_{1} = {\frac{- \tau}{\ln\left( P_{1} \right)}.}} & {{Equation}1}\end{matrix}$

A plurality of the single P₁ measurements can then be plotted together,such as at the plot 300, such as by the measurement component 242, whichcan be converted to estimated T₁s with equation 1. As indicated above,flux tunable measurements of T₁ (Δω_(i)) can also be employed, amongother options.

As shown, the y-axis illustrates frequency space relative to one qubit,and the x-axis represents time, with increments of about 50 hours beingmarked. P₁ is shown as a shaded color scale. The plot 300 exhibitsprominent dips around positive 1 MHz, negative 5-10 MHz, and negative15-20 MHz. The spectral diffusion of the position of the T₁ dips canvary between order of about 1 MHz to about 10 MHz over the 272 hours ofmeasurement providing a qualitative measure of linewidths. Thebackground comprises an ensemble of smaller dips of relaxation, thatalso dynamically evolve with features that are larger than the samplingnoise in the measurement.

That is, as shown, a situation of fluctuating P₁'s (e.g., fluctuatingfrequency space noise) can result in inability to utilize the respectivequbit while the situation persists, otherwise possibly resulting infailure of execution of a quantum circuit employing the particularrespective qubit. That is, the illustrated detection can allow forassessment of the root cause and adjust queue closures for customersemploying a qubit device.

From one or more quantum measurements 240 (e.g., from the readoutcomponent 214), from the representative plot, and/or based on the datafrom which the plot is generated, the measurement component 242 canattain, measure and/or determine one or more energy relaxationmeasurements at the qubit frequency for a qubit and at a plurality ofshifted frequencies for the qubit. The number (e.g., plurality) ofenergy relaxation measurements at the shifted frequencies can beselected based on view of the plot 300, based on historical data, and/orthe like. In one or more embodiments, data from both positive andnegative shifts relative to the qubit frequency can be employed. In oneor more embodiments the range can be asymmetrical about the qubitfrequency (e.g., greater positive or negative range than the other ofpositive or negative range).

Based on these measurements attained by the measurement component 242,the <T₁>_(δω) estimator can be generated by the estimation component246. As alluded to above, an estimator <T₁>_(δω) has been surprisinglydiscovered by the inventors to be a faster estimator of unattainable<T₁> (true average T₁) than existing techniques for obtaining anestimator of average T₁ (denoted herein as <T₁>). The estimatordescribed herein, <T₁>_(δω), is an estimator for <T₁> that can beobtained more quickly than the long time averaging necessary to obtain<T₁>_(Δt). Indeed, the estimator described herein, <T₁>_(δω), caninstead comprise averaging by taking T₁ measurements at multiple offsetfrequencies, Δω_(i), from the qubit frequency, ω_(q), of a qubit, q (ωare expressed typically in Rad/s whereas f=ω/(2π) are expressed in Hz).As used herein, “j” is an index for N different frequencies, where N isthe number of different frequencies measured.

The <T₁>_(δω) estimator can be formed based on Equation 2 withparameters defined here in this list: ω_(q) is qubit frequency, ω_(j) isthe jth qubit frequency shift, δω_(j) is the frequency bin size at thejth frequency shifted location, δω is span of qubit frequency shift, nis the number of spectroscopy time slices, t_(i) is a time slice for thespectroscopy, τ is the decay time at which P₁ was evaluated, P₁(ω_(q)+ω_(j), τ, t_(i)) is the probability of |1> at τ for time stampt_(i) and a frequency shift of ω_(j).

$\begin{matrix}{\left\langle T_{1} \right\rangle_{\delta\omega} = {\frac{1}{n}{\sum}_{i = 1}^{n}\frac{1}{2\delta\omega}{\sum}_{j = {- {\delta\omega}_{-}}}^{\delta\omega_{+}}{T_{1}\left( {{\omega_{q} + \omega_{j}},\tau,t_{i}} \right)}\delta\omega_{j}}} & {{Equation}2}\end{matrix}$

The <T₁>δω estimator of Equation 2 can be obtained, being the estimationof true average relaxation time of the qubit based on the plurality ofall the j energy relaxation measurements. One may obtain T₁(ω_(q)+ω_(j), τ) by converting P₁ (ω_(q)+ω_(j), τ) to a T₁ usingEquation 3 or by any other means of estimating T₁ (e.g., P₁ estimates atdifferent delay times to reconstruct an exponential decay instead ofrelying on one delay time).

$\begin{matrix}{{{T_{1}\left( {{\omega_{q} + \omega_{j}},\tau,t} \right)} = \frac{- \tau}{\ln\left( {P_{1}\left( {{\omega_{q} + \omega_{j}},\tau,t} \right)} \right)}},} & {{Equation}3}\end{matrix}$

where τ is the fixed time delay and t is a time stamp such as t_(i).

As illustrated at Equation 2, a uniform weighting has been applied tothe plurality of energy relaxation measurements (e.g., at the qubitfrequency and at frequencies shifted from the qubit frequency), such asby the weighting component 244. Other weightings can be applied at eachω_(j) in one or more other embodiments (e.g., α_(j)δω_(j) instead ofδω_(j) in Equation 2, where δα_(j) is a more optimized weightingfunction).

Referring next to FIG. 4 , one general proof of concept is illustratedby comparing average P₁s from energy relaxation spectroscopy to the‘true’<P₁>, for which our best estimate of <P₁> is obtained from<T₁>_(Δt) using Equation 1 (in reverse) resulting in <P₁>_(Δt). Theestimator is the uniform average of P₁ (ω_(q)+ω_(j), τ) over all j'sproducing <P₁>_(ω,t). This can be made to correlate with the equivalentbest estimator available of <P₁>_(Δt). At the plot 402, the estimator<P₁>_(Δt) is attained after averaging for about 9 months. That is, wecan compare <listed as <P₁>_(f) in the figure, to <P₁>_(Δt), listed as<P₁>_(T) in the figure. The <P₁>_(ω,t) can be calculated for a delaytime of τ=50 μs for 10 qubits in the device for the first time slice andcutoff frequency δω/2π=+/−5 MHz. As illustrated at FIG. 4 , aqualitatively close agreement for the 10 qubits can be observed.

In the example 404, a <T₁>_(δω) can be estimated for each qubit usingEquation 2. The approximate equivalence of <T₁>_(δω), listed as <T₁>_(f)in the figure, and <T₁>_(Δt) (a 9 month average), listed as <T₁>_(T) inthe figure, is shown in the scatter plot of FIG. 4 (404). T₁(ω_(q)), aT₁ measurement at a single time stamp, and at the qubit frequency foreach qubit in the device, is also shown for reference, in 404, listed as‘T₁ once’. The T₁(ω_(q)) measurement has a greater standard deviationand is a poorer 1:1 agreement with the ‘true’ T₁s. To quantify thisdifference, a correlation between measurements can be quantified by ameasure such as the Pearson R, which can provide a value between −1(completely anticorrelated) to +1 (completely correlated) and where 0means no correlation.

The correlations can be quantified with a Pearson R measure across theten odd-labeled qubits (e.g., Equation 4). Pearson R is a statistic forcorrelations known to one skilled in the art.

$\begin{matrix}{R = {\frac{\sum\limits_{i = 0}^{9}{\left( {\left\langle P_{1} \right\rangle_{T,Q_{i}} - \overset{\_}{\left\langle P_{1} \right\rangle_{T}}} \right)\left( {\left\langle P_{1} \right\rangle_{\omega,t,Q_{i}} - {\overset{\_}{\left\langle P_{1} \right\rangle}}_{\omega,t}} \right)}}{\sqrt{\sum\limits_{i = 0}^{9}{\left( {\left\langle P_{1} \right\rangle_{T,Q_{i}} - \overset{\_}{\left\langle P_{1} \right\rangle_{T}}} \right)^{2}\left( {\left\langle P_{1} \right\rangle_{\omega,t,Q_{i}} - {\overset{\_}{\left\langle P_{1} \right\rangle}}_{\omega,t}} \right)^{2}}}}.}} & {{Equation}4}\end{matrix}$

Briefly, Equation 4 represents a definition of Pearson R measure forevaluating strength of correlations. The sums are evaluated over the 10Qi qubits in the device.

This Equation 4 utilizes P₁ (probability of measuring |1> state) and canbe converted to T₁. <P₁>T refers to the average value of P₁ for the T₁estimator measurements, and <P₁>_(ω,t) is the average value of P₁ fromfrequency measurements. The bar over <P₁> represents an average over allmeasurements.

The resulting Pearson correlation is a normalized covariance between twovariables reflecting a linear correlation from 1 to −1, where R=1 (−1)represents a 100% positive (negative) correlation and R=0 indicates nocorrelation. For a single frequency sweep that takes ˜20 minutes, weobtain 0.76<R<0.84 correlation between <T₁>_(T) and <T₁>_(ω,t) for 0.5MHz<Δω<5 MHz. Using the P₁ values without assuming an exponentialdependence can lead to strong correlations of 0.87<R<0.91. Both of thesecan be substantially stronger than the correlation found between therepresentative instance of T₁ and <T₁>_(T), which was R=0.29

Subsequently, after determination of one or more estimations of trueenergy relaxation times of one qubit, the same operations can beperformed for one or more qubits of the same qubit logic circuit (e.g.,qubit logic circuit 218) and/or for one or more qubits of yet anotherqubit device (e.g., qubit logic circuit). Based on the results, acomparison can be made, such as by the measurement component 242, as towhich qubit device to employ for execution of a particular quantumcircuit. For example, one or more qubits that are desired to be employedof a first device could be understood to have better coherence timesthan one or more qubits that are desired to be employed of a seconddevice, based on the aforedescribed operations. That is, the measurementcomponent 242 can, in one or more embodiments, determine which of a pairof qubit devices to employ for execution of a quantum circuit bycomparing the estimations of the true average relaxation times of thequbits therein.

Indeed, T₁ fluctuations can introduce uncertainty in the coherencebenchmarking, stability of multi-qubit circuit performance and processoptimization of superconducting qubit devices.

Turning now to FIGS. 5A to 6 , as indicated above, to get the T₁measurements in the first instance that can then result in theaforedescribed estimations of true relaxation times of a qubit, initialdiagnostics can be performed. These initial diagnostics employ at leastthe quantum system 201, and are based on use of the AT effect, fluxbias, DC electric field and/or mechanical strain to shift a frequency ofa qubit, thereby allowing the qubit with shifted frequency to beemployed as a probe of the frequency space about the qubit.

Generally, the operations can comprise determining qubit shiftedfrequencies, based on the known shifted frequencies determiningprobabilities P₁ of a qubit being at a particular state at a particulartime, based on the probabilities P₁ determining one or more T₁ (energyrelaxation) times of a qubit from different shifted frequencies, and/orfacilitating postulation of presence of one or more TLSs and/or TLStransitions/fluctuations.

One particular set of diagnostic processes can employ the AT effect, andthus employ off-resonant AT microwave tones to induce an effectivefrequency shift Δω_(q), to thereby analyze the spectral dynamics of T₁times of one or more of the qubits (e.g., qubits 217 of FIG. 2 ).

Referring first to FIG. 5A, energy relaxation spectroscopy employing anAT tone is generally illustrated. Such energy relaxation spectroscopy,employing an AT tone can be employed to understand the frequency spaceof a fixed frequency qubit, absent use of flux tuning, to rapidlydetermine T₁ relaxation times at different shifted frequencies of thequbit, without the need to separately measure (e.g., including waitingfor the excited qubit to again reach ground state) at each differentshifted frequency.

The frequency space of a single qubit is illustrated relative to beingacted upon by an AT tone. The plots 502 of graph 500 illustrate T₁relaxation times of a qubit vs. qubit frequency ω_(q). The plot 504illustrates that in the presence of an AT tone at frequency ω_(s) anddrive amplitude (vertical) Ω_(S), the frequency ω_(q) of the qubitfollows the plot 504 and changes by an amount Δω_(q). It is noted thatTLSs decrease the T₁ relaxation time when on resonance with the qubitfrequency ω_(q), as shown by the dips at the plots 502. Becausefrequencies of TLSs, ω_(TLS), fluctuate in time, the position of a TLS(generally alluded to by dips in T₁) can vary over time, and thus may ormay not affect qubit coherence depending on the time and/or the qubitfrequency shift employed.

That is, a temporary (non-continuous) AT tone can be applied to anexcited qubit with an amount of additional power/amplitude Ω_(S) totemporarily shift the frequency of the qubit according to how muchpower/amplitude Ω_(S) is applied. The shift is generally quadratic, inview of the AT tone. Use of the AT tone can allow for moving the qubitfrequency through the frequency space about the qubit and ideally intoresonance with a TLS. In this manner, frequency space about the qubitfrequency can be probed using the qubit, to detect, after one or morecomputations using the results of measurements of the qubit, where acoherence time of the qubit may be low and/or where a TLS can be at aparticular instant. Indeed, generally, a neighborhood of the unperturbedstate of the qubit can be mapped.

Indeed, without the application of flux bias and inclusion andmodification due to multi-junctions, the neighborhood can more easily beobtained. It is noted, however, that the diagnostic processes describedherein also can function for use with multi-junction qubits.

It also is noted that a diagnostic process could be employed in anembodiment where a continuous AT tone is applied to a qubit. That is thequbit would be continuously shifted, not just temporarily. In such case,the qubit and/or quantum circuit can be recalibrated in that typicalquantum circuits are generally based on non-constantly shifted qubits.

Turning next to FIG. 5B, a pair of pulse sequences are illustrated at520 and 530 that can be applied to a qubit 217, such as by the shiftingcomponent 212, such as via control by the processor 206 and/or quantumoperation component 216.

The pulse sequence 520 represents a Ramsey experiment employing an ATtone. The pulse sequence 520 comprises a first pulse X, such as a π/2pulse, that can be applied to the particular qubit. This first pulse Xcan put the qubit on its equator. After emission of the first pulse X,an AT tone 522 can be applied, also by the shifting component 212, tothe qubit to thereby shift the resonating frequency of the qubit. The ATtone 522 is applied with fixed power Ω_(S) and sweeping of the label Δtin FIG. 5 (also referred to herein as delay times or τ). Generally,thereafter cessation of the second pulse (e.g., the AT tone 522), ameasurement can be taken, such as by the readout component 214 of thequbit. More particularly, a third pulse X can be applied to the qubit,such as another a π/2 pulse. The readout component 214, such as via ameasurement pulse, waveform or other signal applied to the qubit by theshifting component 212, can take a measurement and thereafter determinethe shift of the qubit frequency. The Ramsey fringe can be fit to a sinefunction. The change in frequency (from no AT tone applied) can indicatea change due to the AT tone. For example the fit of the resulting Ramseyfringes can correspond to the frequency shift. This resulting frequencyshift can be employed in subsequent diagnostics, to be describedrelative to additional Figures, as a known shift cause by a particularAT tone 522.

The pulse sequence 530 represents pulses employed for T₁ relaxationspectroscopy with an AT tone. As shown, a first pulse at π can beemitted by the shifting component 212 to the qubit. This first pulse canexcite the qubit to a first state |1>. A second pulse 532, being an ATtone at a fixed frequency ω_(s) can be temporarily emitted by theshifting component 212, to the qubit. This AT tone can be swept overvarying power/amplitudes Ω_(S), to result in decay at a different qubitfrequency (e.g., shifted qubit frequency) ω_(q) of the qubit. That is,by applying the AT tone to the excited qubit, the qubit's frequency canbe shifted. A sweep of Ω_(S) can thus correspond to measurements ofdecay at different qubit frequencies. The resultant measurementinformation of the qubit at the different qubit frequencies, such asattained and measured by the readout component 214, can be employed todetermine probabilities P₁ of the qubit to be at a particular state,such as the |1> state at a particular time while at a single timeinterval, and further to determine a plurality of T₁ times at thedifferent shifted frequencies. This can be completed absent actuallyevaluating the qubit at each of those shifted frequencies for the fullrelaxation time in order to thus attain the relaxation times T₁. Indeed,the sequence 530 at FIG. 5B, and/or a sequence similar thereto, can berun repeatedly, such as in uniform and/or non-uniform increments. Over aperiod of time, where the sequence 530 has been additionally run for thesame particular qubit, predictions can be calculated.

Turning now to FIG. 6 , explanation follows regarding how a single pointon the curve of exponential decay of a qubit state, such as of the |1>state, being a P₁ value, can be employed as a proxy for T₁ at varyingshifted qubit frequencies N. As used herein, P₁ can represent theprobability of finding the qubit in the |1>, or another state, at aparticular qubit frequency ω_(q) at a given time interval. Thisprobability P₁ can be employed to determine the probability of how highthe coherence is for that qubit.

For example, exponential decay of the |1> state can be assumed, with adelay time (e.g., about 50 μs) can be employed after the |1> state isformed, and T₁ can be equal to −τ/ln(P₁). That is, there is a P₁ forevery shifted qubit frequency and every time point at which P₁ ismeasured. P₁ can be a function, such as P₁ (Δω_(t)). A T₁ for eachshifted frequency can be estimated from each P₁, such as employingEquation 5.

$\begin{matrix}{{T_{1}\left( {\Delta\omega} \right)} = {- \frac{\tau}{\ln\left( {P_{1}\left( {\Delta\omega} \right)} \right)}}} & {{Equation}5}\end{matrix}$

where Δω is the frequency shift and t is the fixed time delay.

That is, instead of measuring the entire T₁ decay at any particularshifted qubit frequency, the excited state probability P₁ is employed,after a fixed delay time as a measure of T₁. This method can speed upspectral scans as compared to the existing techniques (measuring theentire T₁ decay at any particular shifted qubit frequency).

Further, the spectral scans (e.g., diagnostic processes) can berepeated, such as at a repetition rate of 1 kHz. That is, additionalaveraging can improve the result of the estimator in Equation 2, wherethe repeated scans correspond to the first sum of Equation 2. One ormore reset techniques known to one having ordinary skill in the art canbe employed to further speed up the repetition rate, thus allowing forprobing faster TLS dynamics. In one embodiment, an amplitude sweep withoff-resonant pulses at fixed detuning (e.g., about +/−50 MHZ) andduration (delay time of about 50 μs) can be employed as the secondpulse, after exciting the qubit with one or more first pulses (which canbe the same or different from one another). See, e.g., pulse sequence530 at FIG. 5B. Such pulsed AT sequence 530 can enable fasterspectroscopy by circumventing re-calibration of the π and π/2 pulses ateach frequency. The amplitude points in the sweep can be related toparticular AT shifts by use of a Ramsey sequence (e.g., pulse sequence520 of FIG. 5B) performed before or after the aforementioned spectralscans. Based on these diagnostic processes, P₁ values can be attained.

That is, at graph 600, plot 604, plotted are P₁ values against change inAT tone frequency Δω_(s)/2π in megahertz (MHz). Plot 604 is for a singledelay time of about 50 μs. Measurements are taken at differentfrequencies of the qubit to get each P₁ value on the plot 604. Forexample, illustrated is probability P₁ of qubit measurement resulting in|1> state (such as over 1000 averages) for an AT tone detuned 50 MHzabove the qubit f01, using the pulse sequence 530 of FIG. 5B. To speedup measurements, P₁ can be used as a proxy for T₁ at a fixed delay timeof 50 us. Generally, delay time can be selected to have high contrastbetween P₁ of about 1 (e.g., delay time of about 0) and P₁ of about 0(e.g., delay time >>T₁). For example, a delay time of about 0.5 T₁ canprovide a reasonable contrast. The X values can be calibrated from Ω_(S)drive amplitude to ω_(q) qubit frequency using the Ramsey experimentpulse sequence 520 of FIG. 5B (e.g., using a Ramsey fringe measurementof qubit frequency as known to one having ordinary skill in the art).Additional X values (values on the x-axis of the figure) can be scaledby the quadratic expression of Equation 6. Put another way, in theX-axis are shifted frequencies of the qubit, measured from a Ramseyexperiment, calibrated using the qubit frequency shift value for everydesired value of power of Ω_(S).

$\begin{matrix}{{{\Delta\omega_{q}} = \frac{\delta_{q}\Omega_{s}^{2}}{2{\Delta_{qs}\left( {\delta_{q} + \Delta_{qs}} \right)}}},} & {{Equation}6}\end{matrix}$

where Δ_(qs) is the detuning (=ω_(q)−ω_(s)), and δ_(q) is theanharmonicity of the qubit given by f12-f01.

As illustrated, the plot 604 comprises a plurality of peaks and valleys.A dip can be representative of a likely TLS.

Furthermore, relative to single points of P₁ on the plot 604, a T₁experiment can be executed, by fixing the frequency shift instead ofpower, and varying the amount of power, and can map a full decay curvefor each of those points, as shown at plots 606, 608 and 610. The T₁experiment can comprise measuring P₁ for different delay times. This canproduce an exponential decay. For example, plots 606, 608, 610illustrate T₁ decay curves from which a T₁ can be extracted (rather thanestimating from a single P₁ at a single delay time).

Accordingly, by being able to shift the frequency of the qubit whileobserving the relaxation at the new shifted frequencies, by employingthe pulse sequence 530, one can determine where qubit coherence will beworse (dips at plot 604) or better, and without direct observance ofdecay at each of the shifted qubit frequencies.

In one or more embodiments, P₁ can be spectrally resolved to about +/225 MHz around the individual qubit frequencies. The narrow frequencyrange combined with measuring non-neighbor sets of qubits simultaneouslycan avoid strong P₁ suppression from resonances with neighboring qubits,with the coupling bus, or with common low-Q parasitic microwave modes.

Next, FIG. 7 illustrates a flow diagram of an example, non-limitingmethod 700 that can facilitate analysis of qubit coherence parameters ofa quantum system, in accordance with one or more embodiments describedherein, such as the non-limiting system 200 of FIG. 2 . While thenon-limiting method 700 is described relative to the non-limiting system200 of FIG. 2 , the non-limiting method 700 can be applicable also toother systems described herein, such as the non-limiting system 100 ofFIG. 1 . Repetitive description of like elements and/or processesemployed in respective embodiments is omitted for sake of brevity.

At 702, the non-limiting method 700 can comprise measuring, by a system(e.g., readout component 214 and/or measurement component 242)operatively coupled to a processor, a plurality of energy relaxationmeasurements comprising at least one measurement at a qubit frequencyfor a qubit and one or more measurements at one or more shiftedfrequencies for the qubit.

At 704, the non-limiting method 700 can comprise determining, by thesystem (e.g., estimation component 246), an estimation of a true averagerelaxation time of the qubit based on the plurality of energy relaxationmeasurements.

At 706, the non-limiting method 700 can comprise employing, by thesystem (e.g., weighting component 244), weightings of the plurality ofenergy relaxation measurements for the determining the estimation of thetrue average relaxation time of the qubit.

At 708, the non-limiting method 700 can comprise determining, by thesystem (e.g., estimation component 246), the estimation of the trueaverage relaxation time of the qubit results from the measurements atthe shifted frequencies for the qubit, offset in the positive direction,the negative direction, or the positive and negative directions relativeto the qubit frequency.

At 710, the non-limiting method 700 can comprise estimating, by thesystem (e.g., estimating component 246), the plurality of energyrelaxation measurements from a measurement of a single decay probabilityof the qubit, assuming an exponential decay.

At 712, the non-limiting method 700 can comprise taking, by the system(e.g., measurement component 242), the plurality of relaxationmeasurements over a range of frequencies that is asymmetrical about thequbit frequency of the qubit.

At 714, the non-limiting method 700 can comprise shifting, by the system(e.g., shifting component 212), the frequency of the qubit by employingflux tuning, an Autler-Townes off-resonant tone, DC electric field ormechanical strain.

At 716, the non-limiting method 700 can comprise determining, by thesystem (e.g., measurement component 242), which of a pair of qubitdevices to employ for execution of a quantum circuit by comparing trueaverage relaxation times of qubits of the pair of qubit devices, whereinthe qubits of the pair of qubit devices comprise the qubit.

In one or more embodiments, the probability can be of the qubit beingfound in another excited state, other than the excited state to whichthe qubit was initially driven prior to application of the second pulse,after a specified time after cessation of the second pulse.

For simplicity of explanation, the computer-implemented andnon-computer-implemented methodologies provided herein are depictedand/or described as a series of acts. It is to be understood that thesubject innovation is not limited by the acts illustrated and/or by theorder of acts, for example acts can occur in one or more orders and/orconcurrently, and with other acts not presented and described herein.Furthermore, not all illustrated acts can be utilized to implement thecomputer-implemented and non-computer-implemented methodologies inaccordance with the described subject matter. In addition, thecomputer-implemented and non-computer-implemented methodologies couldalternatively be represented as a series of interrelated states via astate diagram or events. Additionally, the computer-implementedmethodologies described hereinafter and throughout this specificationare capable of being stored on an article of manufacture to facilitatetransporting and transferring the computer-implemented methodologies tocomputers. The term article of manufacture, as used herein, is intendedto encompass a computer program accessible from any computer-readabledevice or storage media.

The systems and/or devices have been (and/or will be further) describedherein with respect to interaction between one or more components. Suchsystems and/or components can include those components or sub-componentsspecified therein, one or more of the specified components and/orsub-components, and/or additional components. Sub-components can beimplemented as components communicatively coupled to other componentsrather than included within parent components. One or more componentsand/or sub-components can be combined into a single component providingaggregate functionality. The components can interact with one or moreother components not specifically described herein for the sake ofbrevity, but known by those of skill in the art.

In summary, one or more systems, devices, computer program productsand/or computer-implemented methods of use provided herein relate todetermining estimated true relaxation times of qubits absent measurementof entire T₁ decay times of the qubits. A system can comprise a memorythat stores computer executable components; and a processor thatexecutes the computer executable components stored in the memory,wherein the computer executable components are executable to cause, bythe processor, one or more energy relaxation measurements, using a pulsegeneration, at the qubit frequency for a qubit and at a plurality ofshifted frequencies for the qubit, and to determine, by the processor, atrue average relaxation time of the qubit based on the plurality ofenergy relaxation measurements.

Generally, the one or more systems, devices, computer program productsand/or computer-implemented methods of use provided herein can employ aqubit shifted in frequency, such as by flux tuning, by an Autler-Townesoff-resonant tone (AT tone), by DC electric field, by mechanical strain,and/or by another suitable method to probe a frequency space aboutexcitation frequencies of the qubit. Results of the probing can beemployed to determine probabilities of the qubit being at one or moreexcited states at various times and/or at various shifted frequencies ofthe qubit. Further, results of the probing can be employed to forecastestimated true relaxation times of a qubit at one or more frequenciesbased on the frequency neighborhood about the desired one or morefrequencies. Understanding of variance in the probabilities can allowfor a better understanding of whether or not to employ the qubit, and ora respective qubit device comprising the qubit, such as relative to oneor more other qubits and/or qubit devices. These one or more systems,device, computer program products and/or computer-implemented methods ofuse can be employed relative to plural qubits of a qubit device. It isnoted that while the operations described herein can be employed absentapplication of flux bias to the qubits (e.g., absent flux tuning of thequbits) to determine the aforementioned information and results, suchoperations can function by instead employing flux bias, mechanicalstrain and/or DC electric field to shift a qubit frequency.

Accordingly, an advantage of the aforementioned system,computer-implemented method and/or computer program product can be anincrease in understanding of qubit coherence parameters and offluctuations in the qubit coherence parameters, and the subsequentability to employ that information to provide a rapid forecast of qubituseability for an execution of a quantum program. Further advantages cancomprise an ability to rapidly plot energy relaxation of qubits over aplurality of shifted frequencies relative to the qubit frequencies, andalong a range of real time, such as days, weeks and/or months. This plotcan enable understanding of the dynamic frequency space of a qubit.

Yet another advantage of the aforementioned system, computer-implementedmethod and/or computer program product can be ability to use any of fluxtuning, Autler-Townes effect, DC electric field, mechanical strainand/or other suitable method to shift a qubit's frequency for probingthe frequency space about the qubit frequency of the qubit.

One or more embodiments described herein can be, in one or moreembodiments, inherently and/or inextricably tied to computer technologyand cannot be implemented outside of a computing environment. Forexample, one or more processes performed by one or more embodimentsdescribed herein can more efficiently, and even more feasibly, provideprogram and/or program instruction execution, such as relative todetermination of coherence parameters of a qubit of a physical qubitlayout. Systems, computer-implemented methods and/or computer programproducts facilitating performance of these processes are of greatutility in the field of quantum computing and cannot be equallypracticably implemented in a sensible way outside of a computingenvironment.

One or more embodiments described herein can employ hardware and/orsoftware to solve problems that are highly technical, that are notabstract, and that cannot be performed as a set of mental acts by ahuman. For example, a human, or even thousands of humans, cannotefficiently, accurately and/or effectively probe frequency space of aqubit as the one or more embodiments described herein can facilitatethis process. And, neither can the human mind nor a human with pen andpaper probe frequency space of a qubit, as conducted by one or moreembodiments described herein.

In one or more embodiments, one or more of the processes describedherein can be performed by one or more specialized computers (e.g., aspecialized processing unit, a specialized classical computer, aspecialized quantum computer, a specialized hybrid classical/quantumsystem and/or another type of specialized computer) to execute definedtasks related to the one or more technologies describe above. One ormore embodiments described herein and/or components thereof can beemployed to solve new problems that arise through advancements intechnologies mentioned above, employment of quantum computing systems,cloud computing systems, computer architecture and/or anothertechnology.

One or more embodiments described herein can be fully operationaltowards performing one or more other functions (e.g., fully powered on,fully executed and/or another function) while also performing one ormore of the one or more operations, such as quantum and/or non-quantumoperations, described and/or not specifically described herein.

Turning next to FIGS. 8-10 , a detailed description is provided ofadditional context for the one or more embodiments described herein atFIGS. 1-7 .

FIG. 8 and the following discussion are intended to provide a brief,general description of a suitable operating environment 800 in which oneor more embodiments described herein at FIGS. 1-7 can be implemented.For example, one or more components and/or other aspects of embodimentsdescribed herein can be implemented in or be associated with, such asaccessible via, the operating environment 800. Further, while one ormore embodiments have been described above in the general context ofcomputer-executable instructions that can run on one or more computers,those skilled in the art will recognize that one or more embodimentsalso can be implemented in combination with other program modules and/oras a combination of hardware and software.

Generally, program modules include routines, programs, components, datastructures and/or the like, that perform particular tasks and/orimplement particular abstract data types. Moreover, the aforedescribedmethods can be practiced with other computer system configurations,including single-processor or multiprocessor computer systems,minicomputers, mainframe computers, Internet of Things (IoT) devices,distributed computing systems, as well as personal computers, hand-heldcomputing devices, microprocessor-based or programmable consumerelectronics, and/or the like, each of which can be operatively coupledto one or more associated devices.

Computing devices typically include a variety of media, which caninclude computer-readable storage media, machine-readable storage mediaand/or communications media, which two terms are used herein differentlyfrom one another as follows. Computer-readable storage media ormachine-readable storage media can be any available storage media thatcan be accessed by the computer and includes both volatile andnonvolatile media, removable and non-removable media. By way of example,but not limitation, computer-readable storage media and/ormachine-readable storage media can be implemented in connection with anymethod or technology for storage of information such ascomputer-readable and/or machine-readable instructions, program modules,structured data and/or unstructured data.

Computer-readable storage media can include, but are not limited to,random access memory (RAM), read only memory (ROM), electricallyerasable programmable read only memory (EEPROM), flash memory or othermemory technology, compact disk read only memory (CD ROM), digitalversatile disk (DVD), Blu-ray disc (BD) and/or other optical diskstorage, magnetic cassettes, magnetic tape, magnetic disk storage and/orother magnetic storage devices, solid state drives or other solid statestorage devices and/or other tangible and/or non-transitory media whichcan be used to store specified information. In this regard, the terms“tangible” or “non-transitory” herein as applied to storage, memoryand/or computer-readable media, are to be understood to exclude onlypropagating transitory signals per se as modifiers and do not relinquishrights to standard storage, memory and/or computer-readable media thatare not only propagating transitory signals per se.

Computer-readable storage media can be accessed by one or more local orremote computing devices, e.g., via access requests, queries and/orother data retrieval protocols, for a variety of operations with respectto the information stored by the medium.

Communications media typically embody computer-readable instructions,data structures, program modules or other structured or unstructureddata in a data signal such as a modulated data signal, e.g., a carrierwave or other transport mechanism, and includes any information deliveryor transport media. The term “modulated data signal” or signals refersto a signal that has one or more of its characteristics set and/orchanged in such a manner as to encode information in one or moresignals. By way of example, but not limitation, communication media caninclude wired media, such as a wired network, direct-wired connectionand/or wireless media such as acoustic, RF, infrared and/or otherwireless media.

With reference still to FIG. 8 , the example operating environment 800for implementing one or more embodiments of the aspects described hereincan include a computer 802, the computer 802 including a processing unit806, a system memory 804 and/or a system bus 808. One or more aspects ofthe processing unit 806 can be applied to processors such as 106, 136,206 and/or 236 of the non-limiting systems 100 and/or 200. Theprocessing unit 806 can be implemented in combination with and/oralternatively to processors such as 106, 136, 206 and/or 236.

Memory 804 can store one or more computer and/or machine readable,writable and/or executable components and/or instructions that, whenexecuted by processing unit 806 (e.g., a classical processor, a quantumprocessor and/or like processor), can facilitate performance ofoperations defined by the executable component(s) and/or instruction(s).For example, memory 804 can store computer and/or machine readable,writable and/or executable components and/or instructions that, whenexecuted by processing unit 806, can facilitate execution of the one ormore functions described herein relating to non-limiting system 100and/or non-limiting system 200, as described herein with or withoutreference to the one or more figures of the one or more embodiments.

Memory 804 can comprise volatile memory (e.g., random access memory(RAM), static RAM (SRAM), dynamic RAM (DRAM) and/or the like) and/ornon-volatile memory (e.g., read only memory (ROM), programmable ROM(PROM), electrically programmable ROM (EPROM), electrically erasableprogrammable ROM (EEPROM) and/or the like) that can employ one or morememory architectures.

Processing unit 806 can comprise one or more types of processors and/orelectronic circuitry (e.g., a classical processor, a quantum processorand/or like processor) that can implement one or more computer and/ormachine readable, writable and/or executable components and/orinstructions that can be stored at memory 804. For example, processingunit 806 can perform one or more operations that can be specified bycomputer and/or machine readable, writable and/or executable componentsand/or instructions including, but not limited to, logic, control,input/output (I/O), arithmetic and/or the like. In one or moreembodiments, processing unit 806 can be any of one or more commerciallyavailable processors. In one or more embodiments, processing unit 806can comprise one or more central processing unit, multi-core processor,microprocessor, dual microprocessors, microcontroller, System on a Chip(SOC), array processor, vector processor, quantum processor and/oranother type of processor. The examples of processing unit 806 can beemployed to implement one or more embodiments described herein.

The system bus 808 can couple system components including, but notlimited to, the system memory 804 to the processing unit 806. The systembus 808 can comprise one or more types of bus structure that can furtherinterconnect to a memory bus (with or without a memory controller), aperipheral bus and/or a local bus using one or more of a variety ofcommercially available bus architectures. The system memory 804 caninclude ROM 810 and/or RAM 812. A basic input/output system (BIOS) canbe stored in a non-volatile memory such as ROM, erasable programmableread only memory (EPROM) and/or EEPROM, which BIOS contains the basicroutines that help to transfer information among elements within thecomputer 802, such as during startup. The RAM 812 can include ahigh-speed RAM, such as static RAM for caching data.

The computer 802 can include an internal hard disk drive (HDD) 814(e.g., EIDE, SATA), one or more external storage devices 816 (e.g., amagnetic floppy disk drive (FDD), a memory stick or flash drive reader,a memory card reader and/or the like) and/or a drive 820, e.g., such asa solid state drive or an optical disk drive, which can read or writefrom a disk 822, such as a CD-ROM disc, a DVD, a BD and/or the like.Additionally, and/or alternatively, where a solid state drive isinvolved, disk 822 could not be included, unless separate. While theinternal HDD 814 is illustrated as located within the computer 802, theinternal HDD 814 can also be configured for external use in a suitablechassis (not shown). Additionally, while not shown in operatingenvironment 800, a solid state drive (SSD) can be used in addition to,or in place of, an HDD 814. The HDD 814, external storage device(s) 816and drive 820 can be connected to the system bus 808 by an HDD interface824, an external storage interface 826 and a drive interface 828,respectively. The HDD interface 824 for external drive implementationscan include at least one or both of Universal Serial Bus (USB) andInstitute of Electrical and Electronics Engineers (IEEE) 1394 interfacetechnologies. Other external drive connection technologies are withincontemplation of the embodiments described herein.

The drives and their associated computer-readable storage media providenonvolatile storage of data, data structures, computer-executableinstructions, and so forth. For the computer 802, the drives and storagemedia accommodate the storage of any data in a suitable digital format.Although the description of computer-readable storage media above refersto respective types of storage devices, other types of storage mediawhich are readable by a computer, whether presently existing ordeveloped in the future, can also be used in the example operatingenvironment, and/or that any such storage media can containcomputer-executable instructions for performing the methods describedherein.

A number of program modules can be stored in the drives and RAM 812,including an operating system 830, one or more applications 832, otherprogram modules 834 and/or program data 836. All or portions of theoperating system, applications, modules and/or data can also be cachedin the RAM 812. The systems and/or methods described herein can beimplemented utilizing one or more commercially available operatingsystems and/or combinations of operating systems.

Computer 802 can optionally comprise emulation technologies. Forexample, a hypervisor (not shown) or other intermediary can emulate ahardware environment for operating system 830, and the emulated hardwarecan optionally be different from the hardware illustrated in FIG. 8 . Ina related embodiment, operating system 830 can comprise one virtualmachine (VM) of multiple VMs hosted at computer 802. Furthermore,operating system 830 can provide runtime environments, such as the JAVAruntime environment or the .NET framework, for applications 832. Runtimeenvironments are consistent execution environments that can allowapplications 832 to run on any operating system that includes theruntime environment. Similarly, operating system 830 can supportcontainers, and applications 832 can be in the form of containers, whichare lightweight, standalone, executable packages of software thatinclude, e.g., code, runtime, system tools, system libraries and/orsettings for an application.

Further, computer 802 can be enabled with a security module, such as atrusted processing module (TPM). For instance, with a TPM, bootcomponents hash next in time boot components and wait for a match ofresults to secured values before loading a next boot component. Thisprocess can take place at any layer in the code execution stack ofcomputer 802, e.g., applied at application execution level and/or atoperating system (OS) kernel level, thereby enabling security at anylevel of code execution.

An entity can enter and/or transmit commands and/or information into thecomputer 802 through one or more wired/wireless input devices, e.g., akeyboard 838, a touch screen 840 and/or a pointing device, such as amouse 842. Other input devices (not shown) can include a microphone, aninfrared (IR) remote control, a radio frequency (RF) remote controland/or other remote control, a joystick, a virtual reality controllerand/or virtual reality headset, a game pad, a stylus pen, an image inputdevice, e.g., camera(s), a gesture sensor input device, a visionmovement sensor input device, an emotion or facial detection device, abiometric input device, e.g., fingerprint and/or iris scanner, and/orthe like. These and other input devices can be connected to theprocessing unit 806 through an input device interface 844 that can becoupled to the system bus 808, but can be connected by other interfaces,such as a parallel port, an IEEE 1394 serial port, a game port, a USBport, an IR interface, a BLUETOOTH® interface and/or the like.

A monitor 846 or other type of display device can be alternativelyand/or additionally connected to the system bus 808 via an interface,such as a video adapter 848. In addition to the monitor 846, a computertypically includes other peripheral output devices (not shown), such asspeakers, printers and/or the like.

The computer 802 can operate in a networked environment using logicalconnections via wired and/or wireless communications to one or moreremote computers, such as a remote computer(s) 850. The remotecomputer(s) 850 can be a workstation, a server computer, a router, apersonal computer, portable computer, microprocessor-based entertainmentappliance, a peer device and/or other common network node, and typicallyincludes many or all of the elements described relative to the computer802, although, for purposes of brevity, only a memory/storage device 852is illustrated. Additionally, and/or alternatively, the computer 802 canbe coupled (e.g., communicatively, electrically, operatively, opticallyand/or the like) to one or more external systems, sources and/or devices(e.g., classical and/or quantum computing devices, communication devicesand/or like device) via a data cable (e.g., High-Definition MultimediaInterface (HDMI), recommended standard (RS) 232, Ethernet cable and/orthe like).

In one or more embodiments, a network can comprise one or more wiredand/or wireless networks, including, but not limited to, a cellularnetwork, a wide area network (WAN) (e.g., the Internet), or a local areanetwork (LAN). For example, one or more embodiments described herein cancommunicate with one or more external systems, sources and/or devices,for instance, computing devices (and vice versa) using virtually anyspecified wired or wireless technology, including but not limited to:wireless fidelity (Wi-Fi), global system for mobile communications(GSM), universal mobile telecommunications system (UMTS), worldwideinteroperability for microwave access (WiMAX), enhanced general packetradio service (enhanced GPRS), third generation partnership project(3GPP) long term evolution (LTE), third generation partnership project 2(3GPP2) ultra-mobile broadband (UMB), high speed packet access (HSPA),Zigbee and other 802.XX wireless technologies and/or legacytelecommunication technologies, BLUETOOTH®, Session Initiation Protocol(SIP), ZIGBEE®, RF4CE protocol, WirelessHART protocol, 6LoWPAN (IPv6over Low power Wireless Area Networks), Z-Wave, an ANT, anultra-wideband (UWB) standard protocol and/or other proprietary and/ornon-proprietary communication protocols. In a related example, one ormore embodiments described herein can include hardware (e.g., a centralprocessing unit (CPU), a transceiver, a decoder, quantum hardware, aquantum processor and/or the like), software (e.g., a set of threads, aset of processes, software in execution, quantum pulse schedule, quantumcircuit, quantum gates and/or the like) and/or a combination of hardwareand/or software that facilitates communicating information among one ormore embodiments described herein and external systems, sources and/ordevices (e.g., computing devices, communication devices and/or thelike).

The logical connections depicted include wired/wireless connectivity toa local area network (LAN) 854 and/or larger networks, e.g., a wide areanetwork (WAN) 856. LAN and WAN networking environments can becommonplace in offices and companies and can facilitate enterprise-widecomputer networks, such as intranets, all of which can connect to aglobal communications network, e.g., the Internet.

When used in a LAN networking environment, the computer 802 can beconnected to the local network 854 through a wired and/or wirelesscommunication network interface or adapter 858. The adapter 858 canfacilitate wired and/or wireless communication to the LAN 854, which canalso include a wireless access point (AP) disposed thereon forcommunicating with the adapter 858 in a wireless mode.

When used in a WAN networking environment, the computer 802 can includea modem 860 and/or can be connected to a communications server on theWAN 856 via other means for establishing communications over the WAN856, such as by way of the Internet. The modem 860, which can beinternal and/or external and a wired and/or wireless device, can beconnected to the system bus 808 via the input device interface 844. In anetworked environment, program modules depicted relative to the computer802 or portions thereof can be stored in the remote memory/storagedevice 852. The network connections shown are merely exemplary and oneor more other means of establishing a communications link among thecomputers can be used.

When used in either a LAN or WAN networking environment, the computer802 can access cloud storage systems or other network-based storagesystems in addition to, and/or in place of, external storage devices 816as described above, such as but not limited to, a network virtualmachine providing one or more aspects of storage and/or processing ofinformation. Generally, a connection between the computer 802 and acloud storage system can be established over a LAN 854 or WAN 856 e.g.,by the adapter 858 or modem 860, respectively. Upon connecting thecomputer 802 to an associated cloud storage system, the external storageinterface 826 can, such as with the aid of the adapter 858 and/or modem860, manage storage provided by the cloud storage system as it wouldother types of external storage. For instance, the external storageinterface 826 can be configured to provide access to cloud storagesources as if those sources were physically connected to the computer802.

The computer 802 can be operable to communicate with any wirelessdevices and/or entities operatively disposed in wireless communication,e.g., a printer, scanner, desktop and/or portable computer, portabledata assistant, communications satellite, telephone and/or any piece ofequipment or location associated with a wirelessly detectable tag (e.g.,a kiosk, news stand, store shelf and/or the like). This can includeWireless Fidelity (Wi-Fi) and BLUETOOTH® wireless technologies. Thus,the communication can be a predefined structure as with a conventionalnetwork or simply an ad hoc communication between at least two devices.

The illustrated embodiments described herein can be employed relative todistributed computing environments (e.g., cloud computing environments),such as described below with respect to FIG. 9 , where certain tasks areperformed by remote processing devices that are linked through acommunications network. In a distributed computing environment, programmodules can be located both in local and/or remote memory storagedevices.

For example, one or more embodiments described herein and/or one or morecomponents thereof can employ one or more computing resources of thecloud computing environment 950 described below with reference to FIG. 9, and/or with reference to the one or more functional abstraction layers(e.g., quantum software and/or the like) described below with referenceto FIG. 10 , to execute one or more operations in accordance with one ormore embodiments described herein. For example, cloud computingenvironment 950 and/or one or more of the functional abstraction layers1060, 1070, 1080 and/or 1090 can comprise one or more classicalcomputing devices (e.g., classical computer, classical processor,virtual machine, server and/or the like), quantum hardware and/orquantum software (e.g., quantum computing device, quantum computer,quantum processor, quantum circuit simulation software, superconductingcircuit and/or the like) that can be employed by one or more embodimentsdescribed herein and/or components thereof to execute one or moreoperations in accordance with one or more embodiments described herein.For instance, one or more embodiments described herein and/or componentsthereof can employ such one or more classical and/or quantum computingresources to execute one or more classical and/or quantum: mathematicalfunction, calculation and/or equation; computing and/or processingscript; algorithm; model (e.g., artificial intelligence (AI) model,machine learning (ML) model and/or like model); and/or other operationin accordance with one or more embodiments described herein.

It is to be understood that although one or more embodiments describedherein include a detailed description on cloud computing, implementationof the teachings recited herein are not limited to a cloud computingenvironment. Rather, one or more embodiments described herein arecapable of being implemented in conjunction with any other type ofcomputing environment now known or later developed.

Cloud computing is a model of service delivery for enabling convenient,on-demand network access to a shared pool of configurable computingresources (e.g., networks, network bandwidth, servers, processing,memory, storage, applications, virtual machines and/or services) thatcan be rapidly provisioned and released with minimal management effortor interaction with a provider of the service. This cloud model caninclude at least five characteristics, at least three service models,and at least four deployment models.

Characteristics are as follows:

On-demand self-service: a cloud consumer can unilaterally provisioncomputing capabilities, such as server time and network storage, asneeded automatically without requiring human interaction with theservice's provider.

Broad network access: capabilities are available over a network andaccessed through standard mechanisms that promote use by heterogeneousthin or thick client platforms (e.g., mobile phones, laptops, and PDAs).

Resource pooling: the provider's computing resources are pooled to servemultiple consumers using a multi-tenant model, with different physicaland virtual resources dynamically assigned and reassigned according todemand. There is a sense of location independence in that the consumergenerally has no control or knowledge over the exact location of theprovided resources but can specify location at a higher level ofabstraction (e.g., country, state and/or datacenter).

Rapid elasticity: capabilities can be rapidly and elasticallyprovisioned, in one or more cases automatically, to quickly scale outand rapidly released to quickly scale in. To the consumer, thecapabilities available for provisioning can appear to be unlimited andcan be purchased in any quantity at any time.

Measured service: cloud systems automatically control and optimizeresource use by leveraging a metering capability at one or more levelsof abstraction appropriate to the type of service (e.g., storage,processing, bandwidth and/or active user accounts). Resource usage canbe monitored, controlled and/or reported, providing transparency forboth the provider and consumer of the utilized service.

Service Models are as follows:

Software as a Service (SaaS): the capability provided to the consumer isto use the provider's applications running on a cloud infrastructure.The applications are accessible from various client devices through athin client interface such as a web browser (e.g., web-based e-mail).The consumer does not manage or control the underlying cloudinfrastructure including network, servers, operating systems, storageand/or individual application capabilities, with the possible exceptionof limited user-specific application configuration settings.

Platform as a Service (PaaS): the capability provided to the consumer isto deploy onto the cloud infrastructure consumer-created or acquiredapplications created using programming languages and tools supported bythe provider. The consumer does not manage or control the underlyingcloud infrastructure including networks, servers, operating systemsand/or storage, but has control over the deployed applications andpossibly application hosting environment configurations.

Infrastructure as a Service (IaaS): the capability provided to theconsumer is to provision processing, storage, networks and/or otherfundamental computing resources where the consumer can deploy and runarbitrary software, which can include operating systems andapplications. The consumer does not manage or control the underlyingcloud infrastructure but has control over operating systems, storage,deployed applications and/or possibly limited control of selectnetworking components (e.g., host firewalls).

Deployment Models are as follows:

Private cloud: the cloud infrastructure is operated solely for anorganization. It can be managed by the organization or a third party andcan exist on-premises or off-premises.

Community cloud: the cloud infrastructure is shared by severalorganizations and supports a specific community that has shared concerns(e.g., mission, security requirements, policy and/or complianceconsiderations). It can be managed by the organizations or a third partyand can exist on-premises or off-premises.

Public cloud: the cloud infrastructure is made available to the generalpublic or a large industry group and is owned by an organization sellingcloud services.

Hybrid cloud: the cloud infrastructure is a composition of two or moreclouds (private, community or public) that remain unique entities butare bound together by standardized or proprietary technology thatenables data and application portability (e.g., cloud bursting forload-balancing among clouds).

A cloud computing environment is service oriented with a focus onstatelessness, low coupling, modularity and/or semanticinteroperability. At the heart of cloud computing is an infrastructurethat includes a network of interconnected nodes.

Moreover, the non-limiting systems 100 and/or 200 and/or the exampleoperating environment 800 can be associated with and/or be included in adata analytics system, a data processing system, a graph analyticssystem, a graph processing system, a big data system, a social networksystem, a speech recognition system, an image recognition system, agraphical modeling system, a bioinformatics system, a data compressionsystem, an artificial intelligence system, an authentication system, asyntactic pattern recognition system, a medical system, a healthmonitoring system, a network system, a computer network system, acommunication system, a router system, a server system, a highavailability server system (e.g., a Telecom server system), a Web serversystem, a file server system, a data server system, a disk array system,a powered insertion board system, a cloud-based system and/or the like.In accordance therewith, non-limiting systems 100 and/or 200 and/orexample operating environment 800 can be employed to use hardware and/orsoftware to solve problems that are highly technical in nature, that arenot abstract and/or that cannot be performed as a set of mental acts bya human.

Referring now to details of one or more aspects illustrated at FIG. 9 ,the illustrative cloud computing environment 950 is depicted. As shown,cloud computing environment 950 includes one or more cloud computingnodes 910 with which local computing devices used by cloud consumers,such as, for example, personal digital assistant (PDA) or cellulartelephone 954A, desktop computer 954B, laptop computer 954C and/orautomobile computer system 954N can communicate. Although notillustrated in FIG. 9 , cloud computing nodes 910 can further comprise aquantum platform (e.g., quantum computer, quantum hardware, quantumsoftware and/or the like) with which local computing devices used bycloud consumers can communicate. Cloud computing nodes 910 cancommunicate with one another. They can be grouped (not shown) physicallyor virtually, in one or more networks, such as Private, Community,Public, or Hybrid clouds as described hereinabove, or a combinationthereof. This allows cloud computing environment 950 to offerinfrastructure, platforms and/or software as services for which a cloudconsumer does not need to maintain resources on a local computingdevice. It is understood that the types of computing devices 954A-Nshown in FIG. 9 are intended to be illustrative only and that cloudcomputing nodes 910 and cloud computing environment 950 can communicatewith any type of computerized device over any type of network and/ornetwork addressable connection (e.g., using a web browser).

Referring now to details of one or more aspects illustrated at FIG. 10 ,a set 1000 of functional abstraction layers is shown, such as providedby cloud computing environment 950 (FIG. 19 ). One or more embodimentsdescribed herein can be associated with, such as accessible via, one ormore functional abstraction layers described below with reference toFIG. 10 (e.g., hardware and software layer 1060, virtualization layer1070, management layer 1080 and/or workloads layer 1090). It should beunderstood in advance that the components, layers and/or functions shownin FIG. 10 are intended to be illustrative only and embodimentsdescribed herein are not limited thereto. As depicted, the followinglayers and/or corresponding functions are provided:

Hardware and software layer 1060 can include hardware and softwarecomponents. Examples of hardware components include: mainframes 1061;RISC (Reduced Instruction Set Computer) architecture-based servers 1062;servers 1063; blade servers 1064; storage devices 1065; and/or networksand/or networking components 1066. In one or more embodiments, softwarecomponents can include network application server software 1067, quantumplatform routing software 1068; and/or quantum software (not illustratedin FIG. 10 ).

Virtualization layer 1070 can provide an abstraction layer from whichthe following examples of virtual entities can be provided: virtualservers 1071; virtual storage 1072; virtual networks 1073, includingvirtual private networks; virtual applications and/or operating systems1074; and/or virtual clients 1075.

In one example, management layer 1080 can provide the functionsdescribed below. Resource provisioning 1081 can provide dynamicprocurement of computing resources and other resources that can beutilized to perform tasks within the cloud computing environment.Metering and Pricing 1082 can provide cost tracking as resources areutilized within the cloud computing environment, and/or billing and/orinvoicing for consumption of these resources. In one example, theseresources can include one or more application software licenses.Security can provide identity verification for cloud consumers and/ortasks, as well as protection for data and/or other resources. User (orentity) portal 1083 can provide access to the cloud computingenvironment for consumers and system administrators. Service levelmanagement 1084 can provide cloud computing resource allocation and/ormanagement such that required service levels are met. Service LevelAgreement (SLA) planning and fulfillment 1085 can providepre-arrangement for, and procurement of, cloud computing resources forwhich a future requirement is anticipated in accordance with an SLA.

Workloads layer 1090 can provide examples of functionality for which thecloud computing environment can be utilized. Non-limiting examples ofworkloads and functions which can be provided from this layer include:mapping and navigation 1091; software development and lifecyclemanagement 1092; virtual classroom education delivery 1093; dataanalytics processing 1094; transaction processing 1095; and/orapplication transformation software 1096.

The embodiments described herein can be directed to one or more of asystem, a method, an apparatus and/or a computer program product at anypossible technical detail level of integration. The computer programproduct can include a computer readable storage medium (or media) havingcomputer readable program instructions thereon for causing a processorto carry out aspects of the one or more embodiments described herein.The computer readable storage medium can be a tangible device that canretain and store instructions for use by an instruction executiondevice. The computer readable storage medium can be, for example, but isnot limited to, an electronic storage device, a magnetic storage device,an optical storage device, an electromagnetic storage device, asuperconducting storage device and/or any suitable combination of theforegoing. A non-exhaustive list of more specific examples of thecomputer readable storage medium can also include the following: aportable computer diskette, a hard disk, a random access memory (RAM), aread-only memory (ROM), an erasable programmable read-only memory (EPROMor Flash memory), a static random access memory (SRAM), a portablecompact disc read-only memory (CD-ROM), a digital versatile disk (DVD),a memory stick, a floppy disk, a mechanically encoded device such aspunch-cards or raised structures in a groove having instructionsrecorded thereon and/or any suitable combination of the foregoing. Acomputer readable storage medium, as used herein, is not to be construedas being transitory signals per se, such as radio waves and/or otherfreely propagating electromagnetic waves, electromagnetic wavespropagating through a waveguide and/or other transmission media (e.g.,light pulses passing through a fiber-optic cable), and/or electricalsignals transmitted through a wire.

Computer readable program instructions described herein can bedownloaded to respective computing/processing devices from a computerreadable storage medium and/or to an external computer or externalstorage device via a network, for example, the Internet, a local areanetwork, a wide area network and/or a wireless network. The network cancomprise copper transmission cables, optical transmission fibers,wireless transmission, routers, firewalls, switches, gateway computersand/or edge servers. A network adapter card or network interface in eachcomputing/processing device receives computer readable programinstructions from the network and forwards the computer readable programinstructions for storage in a computer readable storage medium withinthe respective computing/processing device. Computer readable programinstructions for carrying out operations of the one or more embodimentsdescribed herein can be assembler instructions,instruction-set-architecture (ISA) instructions, machine instructions,machine dependent instructions, microcode, firmware instructions,state-setting data, configuration data for integrated circuitry, and/orsource code and/or object code written in any combination of one or moreprogramming languages, including an object oriented programming languagesuch as Smalltalk, C++ or the like, and/or procedural programminglanguages, such as the “C” programming language and/or similarprogramming languages. The computer readable program instructions canexecute entirely on a computer, partly on a computer, as a stand-alonesoftware package, partly on a computer and/or partly on a remotecomputer or entirely on the remote computer and/or server. In the latterscenario, the remote computer can be connected to a computer through anytype of network, including a local area network (LAN) and/or a wide areanetwork (WAN), and/or the connection can be made to an external computer(for example, through the Internet using an Internet Service Provider).In one or more embodiments, electronic circuitry including, for example,programmable logic circuitry, field-programmable gate arrays (FPGA)and/or programmable logic arrays (PLA) can execute the computer readableprogram instructions by utilizing state information of the computerreadable program instructions to personalize the electronic circuitry,in order to perform aspects of the one or more embodiments describedherein.

Aspects of the one or more embodiments described herein are describedwith reference to flowchart illustrations and/or block diagrams ofmethods, apparatus (systems), and computer program products according toone or more embodiments described herein. It will be understood thateach block of the flowchart illustrations and/or block diagrams, andcombinations of blocks in the flowchart illustrations and/or blockdiagrams, can be implemented by computer readable program instructions.These computer readable program instructions can be provided to aprocessor of a general purpose computer, special purpose computer and/orother programmable data processing apparatus to produce a machine, suchthat the instructions, which execute via the processor of the computeror other programmable data processing apparatus, can create means forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks. These computer readable program instructionscan also be stored in a computer readable storage medium that can directa computer, a programmable data processing apparatus and/or otherdevices to function in a particular manner, such that the computerreadable storage medium having instructions stored therein can comprisean article of manufacture including instructions which can implementaspects of the function/act specified in the flowchart and/or blockdiagram block or blocks. The computer readable program instructions canalso be loaded onto a computer, other programmable data processingapparatus and/or other device to cause a series of operational acts tobe performed on the computer, other programmable apparatus and/or otherdevice to produce a computer implemented process, such that theinstructions which execute on the computer, other programmable apparatusand/or other device implement the functions/acts specified in theflowchart and/or block diagram block or blocks.

The flowcharts and block diagrams in the figures illustrate thearchitecture, functionality and/or operation of possible implementationsof systems, computer-implementable methods and/or computer programproducts according to one or more embodiments described herein. In thisregard, each block in the flowchart or block diagrams can represent amodule, segment and/or portion of instructions, which comprises one ormore executable instructions for implementing the specified logicalfunction(s). In one or more alternative implementations, the functionsnoted in the blocks can occur out of the order noted in the Figures. Forexample, two blocks shown in succession can be executed substantiallyconcurrently, and/or the blocks can sometimes be executed in the reverseorder, depending upon the functionality involved. It will also be notedthat each block of the block diagrams and/or flowchart illustration,and/or combinations of blocks in the block diagrams and/or flowchartillustration, can be implemented by special purpose hardware-basedsystems that can perform the specified functions and/or acts and/orcarry out one or more combinations of special purpose hardware and/orcomputer instructions.

While the subject matter has been described above in the general contextof computer-executable instructions of a computer program product thatruns on a computer and/or computers, those skilled in the art willrecognize that the one or more embodiments herein also can beimplemented in combination with one or more other program modules.Generally, program modules include routines, programs, components, datastructures and/or the like that perform particular tasks and/orimplement particular abstract data types. Moreover, the aforedescribedcomputer-implemented methods can be practiced with other computer systemconfigurations, including single-processor and/or multiprocessorcomputer systems, mini-computing devices, mainframe computers, as wellas computers, hand-held computing devices (e.g., PDA, phone),microprocessor-based or programmable consumer and/or industrialelectronics and/or the like. The illustrated aspects can also bepracticed in distributed computing environments in which tasks areperformed by remote processing devices that are linked through acommunications network. However, one or more, if not all aspects of theone or more embodiments described herein can be practiced on stand-alonecomputers. In a distributed computing environment, program modules canbe located in both local and remote memory storage devices.

As used in this application, the terms “component,” “system,”“platform,” “interface,” and/or the like, can refer to and/or caninclude a computer-related entity or an entity related to an operationalmachine with one or more specific functionalities. The entitiesdescribed herein can be either hardware, a combination of hardware andsoftware, software, or software in execution. For example, a componentcan be, but is not limited to being, a process running on a processor, aprocessor, an object, an executable, a thread of execution, a programand/or a computer. By way of illustration, both an application runningon a server and the server can be a component. One or more componentscan reside within a process and/or thread of execution and a componentcan be localized on one computer and/or distributed between two or morecomputers. In another example, respective components can execute fromvarious computer readable media having various data structures storedthereon. The components can communicate via local and/or remoteprocesses such as in accordance with a signal having one or more datapackets (e.g., data from one component interacting with anothercomponent in a local system, distributed system and/or across a networksuch as the Internet with other systems via the signal). As anotherexample, a component can be an apparatus with specific functionalityprovided by mechanical parts operated by electric or electroniccircuitry, which is operated by a software and/or firmware applicationexecuted by a processor. In such a case, the processor can be internaland/or external to the apparatus and can execute at least a part of thesoftware and/or firmware application. As yet another example, acomponent can be an apparatus that provides specific functionalitythrough electronic components without mechanical parts, where theelectronic components can include a processor and/or other means toexecute software and/or firmware that confers at least in part thefunctionality of the electronic components. In an aspect, a componentcan emulate an electronic component via a virtual machine, e.g., withina cloud computing system.

In addition, the term “or” is intended to mean an inclusive “or” ratherthan an exclusive “or.” That is, unless specified otherwise, or clearfrom context, “X employs A or B” is intended to mean any of the naturalinclusive permutations. That is, if X employs A; X employs B; or Xemploys both A and B, then “X employs A or B” is satisfied under any ofthe foregoing instances. Moreover, articles “a” and “an” as used in thesubject specification and annexed drawings should generally be construedto mean “one or more” unless specified otherwise or clear from contextto be directed to a singular form. As used herein, the terms “example”and/or “exemplary” are utilized to mean serving as an example, instance,or illustration. For the avoidance of doubt, the subject matterdescribed herein is not limited by such examples. In addition, anyaspect or design described herein as an “example” and/or “exemplary” isnot necessarily to be construed as preferred or advantageous over otheraspects or designs, nor is it meant to preclude equivalent exemplarystructures and techniques known to those of ordinary skill in the art.

As it is employed in the subject specification, the term “processor” canrefer to substantially any computing processing unit and/or devicecomprising, but not limited to, single-core processors;single-processors with software multithread execution capability;multi-core processors; multi-core processors with software multithreadexecution capability; multi-core processors with hardware multithreadtechnology; parallel platforms; and/or parallel platforms withdistributed shared memory. Additionally, a processor can refer to anintegrated circuit, an application specific integrated circuit (ASIC), adigital signal processor (DSP), a field programmable gate array (FPGA),a programmable logic controller (PLC), a complex programmable logicdevice (CPLD), a discrete gate or transistor logic, discrete hardwarecomponents, and/or any combination thereof designed to perform thefunctions described herein. Further, processors can exploit nano-scalearchitectures such as, but not limited to, molecular and quantum-dotbased transistors, switches and/or gates, in order to optimize spaceusage and/or to enhance performance of related equipment. A processorcan be implemented as a combination of computing processing units.

Herein, terms such as “store,” “storage,” “data store,” data storage,”“database,” and substantially any other information storage componentrelevant to operation and functionality of a component are utilized torefer to “memory components,” entities embodied in a “memory,” orcomponents comprising a memory. Memory and/or memory componentsdescribed herein can be either volatile memory or nonvolatile memory orcan include both volatile and nonvolatile memory. By way ofillustration, and not limitation, nonvolatile memory can include readonly memory (ROM), programmable ROM (PROM), electrically programmableROM (EPROM), electrically erasable ROM (EEPROM), flash memory and/ornonvolatile random access memory (RAM) (e.g., ferroelectric RAM (FeRAM).Volatile memory can include RAM, which can act as external cache memory,for example. By way of illustration and not limitation, RAM can beavailable in many forms such as synchronous RAM (SRAM), dynamic RAM(DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM),enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), direct Rambus RAM(DRRAM), direct Rambus dynamic RAM (DRDRAM) and/or Rambus dynamic RAM(RDRAM). Additionally, the described memory components of systems and/orcomputer-implemented methods herein are intended to include, withoutbeing limited to including, these and/or any other suitable types ofmemory.

What has been described above includes mere examples of systems andcomputer-implemented methods. It is, of course, not possible to describeevery conceivable combination of components and/or computer-implementedmethods for purposes of describing the one or more embodiments, but oneof ordinary skill in the art can recognize that many furthercombinations and/or permutations of the one or more embodiments arepossible. Furthermore, to the extent that the terms “includes,” “has,”“possesses,” and the like are used in the detailed description, claims,appendices and/or drawings such terms are intended to be inclusive in amanner similar to the term “comprising” as “comprising” is interpretedwhen employed as a transitional word in a claim.

The descriptions of the one or more embodiments have been presented forpurposes of illustration but are not intended to be exhaustive orlimited to the embodiments described herein. Many modifications andvariations will be apparent to those of ordinary skill in the artwithout departing from the scope and spirit of the describedembodiments. The terminology used herein was chosen to best explain theprinciples of the embodiments, the practical application and/ortechnical improvement over technologies found in the marketplace, and/orto enable others of ordinary skill in the art to understand theembodiments described herein.

What is claimed is:
 1. A system, comprising: a memory that storescomputer executable components; and a processor that executes thecomputer executable components stored in the memory, wherein thecomputer executable components are executable to: cause, by theprocessor, one or more energy relaxation measurements, using a pulsegeneration, at the qubit frequency for a qubit and at a plurality ofshifted frequencies for the qubit; and determine, by the processor, atrue average relaxation time of the qubit based on the plurality ofenergy relaxation measurements.
 2. The system of claim 1, wherein thecomputer executable components are further executable to: apply, by theprocessor, weights to one or more of the energy relaxation measurements,wherein the weights are employed, by the processor, to determine theestimation of the true average relaxation time of the qubit.
 3. Thesystem of claim 1, wherein the estimation of the true average relaxationtime of the qubit results from the measurements at the shiftedfrequencies for the qubit, offset in the positive direction, thenegative direction, or the positive and negative directions relative tothe qubit frequency.
 4. The system of claim 1, wherein the computerexecutable components are further executable to: determine, by theprocessor, the one or more energy relaxation measurements from ameasurement of a single decay probability of the qubit, assuming anexponential decay.
 5. The system of claim 1, wherein a range offrequencies over which the plurality of relaxation measurements aretaken is asymmetrical about the qubit frequency of the qubit.
 6. Thesystem of claim 1, wherein the computer executable components arefurther executable to: cause, by the processor, a shift of the qubitfrequency of the qubit to the plurality of shifted frequencies byemploying a frequency shifting method based on flux tuning, anAutler-Townes off-resonant tone, DC electric field, or mechanicalstrain.
 7. The system of claim 1, wherein the computer executablecomponents are further executable to: determine, by the processor, oneor more energy relaxation measurements at the qubit frequency foranother qubit and at a plurality of shifted frequencies for the anotherqubit, determine, by the processor, an estimation of a true averagerelaxation time of the another qubit based on the plurality of energyrelaxation measurements, and determine, by the processor, which of thequbit or the another qubit to employ for execution of a quantum circuitby comparing the estimations of the true average relaxation times of thequbit and of the another qubit.
 8. A computer-implemented method,comprising: measuring, by a system operatively coupled to a processor, aplurality of energy relaxation measurements comprising at least onemeasurement at a qubit frequency for a qubit and one or moremeasurements at one or more shifted frequencies for the qubit; anddetermining, by the system, an estimation of a true average relaxationtime of the qubit based on the plurality of energy relaxationmeasurements.
 9. The computer-implemented method of claim 8, whereindetermining the estimation of the true average relaxation time of thequbit comprises: employing, by the system, weightings of the pluralityof energy relaxation measurements.
 10. The computer-implemented methodof claim 8, wherein the estimation of the true average relaxation timeof the qubit results from the measurements at the shifted frequenciesfor the qubit, offset in the positive direction, the negative direction,or the positive and negative directions relative to the qubit frequency.11. The computer-implemented method of claim 8, wherein determining theplurality of energy relaxation measurements at the qubit unperturbedfrequency for the qubit comprises: estimating, by the system, theplurality of energy relaxation measurements from a measurement of asingle decay probability of the qubit, assuming an exponential decay.12. The computer-implemented method of claim 8, wherein a range offrequencies over which the plurality of relaxation measurements aretaken is asymmetrical about the qubit frequency of the qubit.
 13. Thecomputer-implemented method of claim 8, further comprising: shifting, bythe system, the frequency of the qubit by employing a frequency shiftingmethod based on flux tuning, an Autler-Townes off-resonant tone, DCelectric field, or mechanical strain.
 14. The computer-implementedmethod of claim 8, determining, by the system, which of a pair of qubitdevices to employ for execution of a quantum circuit by comparingestimations of the true average relaxation times of qubits of the pairof qubit devices, wherein the qubit is comprised by one qubit device ofthe pair of qubit devices, and wherein the estimations of the trueaverage relaxation times comprise the estimation of the true averagerelaxation time of the qubit.
 15. A computer program productfacilitating a process to determine an estimated true relaxation time ofa qubit, the computer program product comprising a computer readablestorage medium having program instructions embodied therewith, theprogram instructions executable by a processor to cause the processorto: measure, by the processor, a plurality of energy relaxationmeasurements comprising at least one measurement at a qubit frequencyfor a qubit and one or more measurements at one or more shiftedfrequencies for the qubit; and determine, by the processor, anestimation of a true average relaxation time of the qubit based on theplurality of energy relaxation measurements.
 16. The computer programproduct of claim 15, wherein the program instructions are furtherexecutable by the processor to cause the processor to: employ, by theprocessor, weightings of the plurality of energy relaxation measurementsto determine the estimation of the true average relaxation time of thequbit.
 17. The computer program product of claim 15, wherein theestimation of the true average relaxation time of the qubit results fromthe measurements at the shifted frequencies for the qubit, offset in thepositive direction, the negative direction, or the positive and negativedirections relative to the qubit frequency.
 18. The computer programproduct of claim 15, wherein the program instructions are furtherexecutable by the processor to cause the processor to: estimating, bythe processor, the plurality of energy relaxation measurements at thequbit unperturbed frequency for the qubit from a measurement of a singledecay probability of the qubit, assuming an exponential decay.
 19. Thecomputer program product of claim 15, wherein a range of frequenciesover which the plurality of relaxation measurements are taken isasymmetrical about the qubit frequency of the qubit.
 20. The computerprogram product of claim 15, wherein the program instructions arefurther executable by the processor to cause the processor to: causeshifting, by the processor, of the frequency of the qubit by employing afrequency shifting method based on flux tuning, an Autler-Townesoff-resonant tone, DC electric field, or mechanical strain.